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if tanx=a/b,prove that asin2x+bcos2x=b............prove it

if tanx=a/b,prove that asin2x+bcos2x=b............prove it

Grade:11

1 Answers

Akash Ojha
20 Points
3 years ago
Since tanx=a/b =>a = btanx...(1)Now, asin2x + bcos2x = a(2sinxcosx) + b(1- sin^2x)=2asinxcosx + b - bsin^2x=2sinx (acosx - bsinx) + b=2sinx (btanxcosx - bsinx) + b ...(from (1))=2sinx (bsinx - bsinx) + b=2sinx (0) + b=bHence, proved.

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