Question

Solve: tan(x) – cos2(x) = sin2(x)

Answer 1

Answer:$x=\frac{\pi}{4}$

Step-by-step explanation:

`Writing tan and cos in form of sin

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

$\frac{sinx}{cosx}-1+2sin^2x=2sinxcosx$

$\frac{sinx-cosx}{cosx}=2sinx\left ( cosx-sinx\right )$

$2sinx\left ( cosx-sinx\right )-\frac{sinx-cosx}{cosx}=0$

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

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

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

cosx-sinx=0

tanx=1,$x=\frac{\pi}{4}$

similarly

$x=n\pi +\frac{\pi}{4}$

For 2sinxcosx+1=0

sin2x=-1

$2x=\frac{3\pi}{2}$

but this value is not satisfied by equation thus

$x=n\pi +\frac{\pi}{4}$

Answer 2

Answer:

pi/4 + kpi (choice #1)

Step-by-step explanation: