Question

Solve: tan(x) – cos2(x) = sin2(x)

Answer 1

pi/4 + kpi (choice #1)

Explanation:

Answer 2

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)`