Question

Verify the following identity. Show all work for credit.

(sec\theta -cos\theta )/(sec\theta )=sin^(2)\theta

Answer 1

Sec 0 divided by sec 0 = 2 cos = sin
Sin2 =0

Answer 2

`\\ \rm\Rrightarrow (secA-cosA)/(secA)`

`\\ \rm\Rrightarrow (1/cosA-cosA)/(secA)`

`\\ \rm\Rrightarrow (1-cosA/cosA)/(secA)`

`\\ \rm\Rrightarrow (2sin^2(A/2)/cosA)/(1/cosA)`

`\\ \rm\Rrightarrow 2sin^2(A/2)`

`\\ \rm\Rrightarrow Sin^2A`

Proved