Question

IF tanx=a/b then prove that acos2x+bsin2x=a

Answer 1

Step-by-step explanation:

=bcos2x+asin2x

=b[(1-tan^2x)/(1+tan^2x)]+a[2tanx/(1+tan^2x)

=1/(1+tan^2x)[b-btan^2x+2atanx]

=1/1+(a/b)^2[b-b(a/b)+2a×a/b

=b^2/a^2+b^2[b-a^2/b+2a^2/b

=b^2/a^2+b^2[b^2+a^2/b]

=b