cos(+pi/2-theta)/csctheta+cos^2theta

Answer 1

cos(π/2 - Ø) = sinØ , complementary angle property

then
cos(+pi/2-theta)/csctheta+cos^2theta
= cos(π/2-Ø) * 1/cscØ + cos^2 Ø
= sinØ ( sinØ) + cos^2 Ø
= sin^2 Ø + cos^2 Ø
= 1