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CBSE Class 11-science Answered

Show that (1+cos x)3/2(1- cos x)1/2​=sin x(1+cos x)
Asked by soumen_tiku | 08 Jun, 2018, 11:51: PM
answered-by-expert Expert Answer
begin mathsize 16px style left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent equals open parentheses 2 cos to the power of 2 space end exponent straight x over 2 close parentheses to the power of 3 over 2 end exponent open parentheses 2 sin squared straight x over 2 close parentheses to the power of 1 half end exponent space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 space and space 1 space minus space cosx space equals 2 sin squared straight x over 2 space equals 2 to the power of 3 over 2 end exponent space cos cubed straight x over 2 space cross times space square root of 2 space sin straight x over 2 equals 2 sin straight x over 2 cos straight x over 2 space cross times 2 cos squared straight x over 2 space space space space space space space space space space space space space space space space space space space space space space space 2 sinx divided by 2 cosx divided by 2 space equals space sinx space equals sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 rightwards double arrow space left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent space equals space sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space end stylebegin mathsize 16px style left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent equals open parentheses 2 cos to the power of 2 space end exponent straight x over 2 close parentheses to the power of 3 over 2 end exponent open parentheses 2 sin squared straight x over 2 close parentheses to the power of 1 half end exponent space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 space and space 1 space minus space cosx space equals 2 sin squared straight x over 2 space equals 2 to the power of 3 over 2 end exponent space cos cubed straight x over 2 space cross times space square root of 2 space sin straight x over 2 equals 2 sin straight x over 2 cos straight x over 2 space cross times 2 cos squared straight x over 2 space space space space space space space space space space space space space space space space space space space space space space space 2 sinx divided by 2 cosx divided by 2 space equals space sinx space equals sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 rightwards double arrow space left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent space equals space sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space end stylebegin mathsize 16px style left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent equals open parentheses 2 cos to the power of 2 space end exponent straight x over 2 close parentheses to the power of 3 over 2 end exponent open parentheses 2 sin squared straight x over 2 close parentheses to the power of 1 half end exponent space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 space and space 1 space minus space cosx space equals 2 sin squared straight x over 2 space equals 2 to the power of 3 over 2 end exponent space cos cubed straight x over 2 space cross times space square root of 2 space sin straight x over 2 equals 2 sin straight x over 2 cos straight x over 2 space cross times 2 cos squared straight x over 2 space space space space space space space space space space space space space space space space space space space space space space space 2 sinx divided by 2 cosx divided by 2 space equals space sinx space equals sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 rightwards double arrow space left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent space equals space sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space end stylebegin mathsize 16px style left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent equals open parentheses 2 cos to the power of 2 space end exponent straight x over 2 close parentheses to the power of 3 over 2 end exponent open parentheses 2 sin squared straight x over 2 close parentheses to the power of 1 half end exponent space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 space and space 1 space minus space cosx space equals 2 sin squared straight x over 2 space equals 2 to the power of 3 over 2 end exponent space cos cubed straight x over 2 space cross times space square root of 2 space sin straight x over 2 equals 2 sin straight x over 2 cos straight x over 2 space cross times 2 cos squared straight x over 2 space space space space space space space space space space space space space space space space space space space space space space space 2 sinx divided by 2 cosx divided by 2 space equals space sinx space equals sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 1 thin space plus thin space cosx space equals space 2 cos to the power of 2 space end exponent straight x over 2 rightwards double arrow space left parenthesis 1 thin space plus thin space cosx right parenthesis to the power of 3 over 2 end exponent left parenthesis 1 space minus space cosx right parenthesis to the power of 1 half end exponent space equals space sinx space cross times left parenthesis 1 space plus thin space cosx right parenthesis space space space space space space space space space space space space end style
Answered by Sneha shidid | 11 Jun, 2018, 11:23: AM

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