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CBSE Class 10 Answered

If √3 tan β = 3 sin β, prove that sin^2 β - cos^2 β = 1/3.
Asked by arup_chakraborty2007 | 10 Nov, 2017, 02:52: PM
answered-by-expert Expert Answer
begin mathsize 16px style square root of 3 space tanβ equals 3 sinβ rightwards double arrow fraction numerator square root of 3 over denominator 3 end fraction equals sinβ cross times cosβ over sinβ rightwards double arrow fraction numerator 1 over denominator square root of 3 end fraction space equals space cosβ rightwards double arrow space cos squared straight beta equals 1 third Using space sin squared straight beta plus cos squared straight beta space equals 1 sin squared straight beta space equals space 1 minus cos squared straight beta space sin squared straight beta space equals 1 minus open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses squared sin squared straight beta space equals 1 minus 1 third sin squared straight beta space equals 2 over 3 rightwards double arrow sin squared straight beta space minus space cos squared straight beta space equals space 2 over 3 space minus 1 third rightwards double arrow sin squared straight beta space minus space cos squared straight beta space equals 1 third space end style
Answered by Sneha shidid | 08 Dec, 2017, 04:56: PM

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