Question

Show that: cosec²theta -tan²(90-theta)= sin²theta+ sin(90-theta)

Answer 1

tan2 theta= cot2(90deg-theta) hence , tan2(90deg -theta) = cot 2 theta

therefore LHS (left side) = cosec2 theta -cot2theta = 1 (by theorem cosec2 theta = 1 + cot2theta)

cos2 theta= sin2(90deg-theta), hence sin2(90deg-theta)= cos2 theta,

hence in RHS ,= sin2 theta +sin2(90deg-theta)=sin2 theta +cos2 theta= 1 (by theorem sin2theta +cos2 theta =1)

hence LHS = RHS

Answer 2

here is your answer