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If cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2...

If `cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2x` is equal to

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GIven `cos2x+2cosx=1`
=`2cos^2x-1+2cosx=1`
=`2cos^2x+2cosx=1+1`
=`2cos^2x+2cosx=2`
=`cos^2x+cosx=1........(i)`
Now as given`(2-cos^2x)sin^2x` =`(2-cos^2x)(1-cos^2x)` =`(2-(1-cosx))(1-(1-cosx))`[by equation (i)] ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
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  11. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

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  12. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

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