Solve: tan(x) – cos2(x) = sin2(x)

Question

asked Aug 16, 2019 168k views

2 Answers

Blow ThemUp · Answer 1 · 2019-08-22T16:11:08+0000

Answer:
$x=(\pi)/(4)$

Explanation:

`Writing tan and cos in form of sin

$(sinx)/(cosx)-\left ( 1-2sin^2x\right )=2sinxcosx$

(sinx)/(cosx)-1+2sin^2x=2sinxcosx

$(sinx-cosx)/(cosx)=2sinx\left ( cosx-sinx\right )$

$2sinx\left ( cosx-sinx\right )-(sinx-cosx)/(cosx)=0$

$\left ( cosx-sinx\right )\left [ 2sinx+(1)/(cosx)\right ]=0$

$\left ( cosx-sinx\right )\left [ (2sinxcosx+1)/(cosx)\right ]=0$

so cosx-sinx=0 or 2sinxcosx+1=0 and cosx is not equals to zero

cosx-sinx=0

tanx=1,
$x=(\pi)/(4)$

similarly

$x=n\pi +(\pi)/(4)$

For 2sinxcosx+1=0

sin2x=-1

$2x=(3\pi)/(2)$

but this value is not satisfied by equation thus

$x=n\pi +(\pi)/(4)$