Verify each identity a sec2theta 1cos2theta sin2theta b si

Verify each identity a. (.sec^2theta - 1)cos^2theta = sin^2theta b. sin theta - sin theta cos^2theta = sin^3theta c. csc theta - cos theta cot theta = sin theta d. cot^2 theta csc^2theta - cot^2theta = cot^4theta

Solution

a)(sec² -1)cos²

=((1/cos²) -1)cos²

=((1-cos²)cos²)cos²

=(1-cos²) [since sin² +cos²=1 is identity]

=sin²

b)sin -sincos²

=sin(1-cos²)

=sin(sin²)

=sin³

c)csc-coscot

=(1/sin)- cos(cos/sin)

=(1/sin)-(cos²/sin)

=(1-cos²)/sin

=sin²/sin

=sin

d)cot²csc² -cot²

=cot²(csc² -1) [since csc² -cot² =1 is identity]

=cot²cot²

=cot⁴