Question

Prove that (cosectheta-sintheta)(secthata-costheta)=1/tantheta+cottheta

Answer 1

Hallo friend here is the answer.......
L.H.S.
(cosec theta-sin theta)(sec theta-cos theta)
={(1/sin theta)-sin theta}{(1-cos theta)-cos theta}
=(1-sin^2 theta/sin theta)(1-cos^2 theta/cos theta)
=(cos^2 theta/sin theta)(sin^2 theta/cos theta)
=cos theta× sin theta

R.H.S.
1/tan theta+cot theta
=1/(sin theta/cos theta)+( cos theta/sin theta)
=1/(sin^2 theta+cos^2 theta/cos theta×sin theta)
=cos theta×sin theta

so,L.H.S.=R.H.S.[proved]
Hope it will help you