Question

Prove that ?

tan^2.sin^2 +cos^2+2sin^2=sec^2

Answer 1

Please see explanation section.
`tan^2color(red)(x)sin^2color(red)(x)+cos^2color(red)(x)+2sin^2color(red)(x)=sec^2color(red)(x)`

Explanation:

I think the Question is:
`tan^2xsin^2x+cos^2x+2sin^2x=sec^2x`
`LHS=tan^2xsin^2x+cos^2x+2sin^2x` `=tan^2xsin^2x+color(red)(cos^2x+sin^2x)+sin^2x` `=tan^2xsin^2x+sin^2x+color(red)(1)`
`=sin^2xcolor(red)((tan^2x+1))+1`
`=sin^2x*color(red)(sec^2x)+1`
`=sin^2x/cos^2x+1`
`=tan^2x+1`
`=sec^2x`
`=RHS`