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Home / Doubts and Solutions/JEE FOUNDATION/Class 9/Mathematics

If cos2A+2sin2A+3cos2A+4sin2A+….(200 terms)=10025,where A is an acute angle,find the value of sinA-cosA

Asked by Sunita 30th December 2017, 10:24 AM
Answered by Expert
Answer:
begin mathsize 16px style cos squared space straight A plus 2 sin squared straight A plus 3 cos squared straight A plus 4 sin squared straight A plus....... left parenthesis 200 space terms right parenthesis equals 10025 rightwards double arrow left parenthesis cos squared space straight A plus 3 cos squared straight A plus.......100 space terms right parenthesis plus left parenthesis 2 sin squared straight A plus 4 sin squared straight A plus.......200 space terms right parenthesis equals 10025 rightwards double arrow 100 squared space cos squared straight A plus left parenthesis 100 squared plus 100 right parenthesis space sin squared thin space straight A equals 10025 rightwards double arrow 10000 space left parenthesis cos squared straight A plus sin squared straight A right parenthesis plus 100 space sin squared straight A equals 10025 rightwards double arrow 100 space sin squared straight A equals 25 rightwards double arrow sin squared straight A equals 1 fourth rightwards double arrow sin space straight A equals 1 half rightwards double arrow straight A space equals space 30 degree space space left parenthesis since space straight A thin space is space acute right parenthesis Hence comma space sin space straight A space minus space cos space straight A equals sin space 30 degree minus cos space 30 degree equals 1 half minus fraction numerator square root of 3 over denominator 2 end fraction equals fraction numerator 1 minus square root of 3 over denominator 2 end fraction end style
Answered by Expert 30th December 2017, 3:13 PM
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