Question

(sec theta + cosec theta ) (sin theta+ cos theta)=sec theta cosec theta +2

Answer 1

L.H.S.=
=(1/cos theta + 1/sin theta) (sin theta + cos theta)
= (sin theta+cos theta/ cos theta sin theta) ( sin theta + cos theta)
= (sin theta + cos theta)^2/cos theta sin theta
=(sin^2 theta + cos^2 theta+2cos theta sin theta) / cos theta sin theta
= (1 + 2cos theta sin theta) /cos theta sin theta
= 1/cos theta sin theta + 2sin theta cos theta/cos theta sin theta
= 1 / cos theta sin theta + 2
=sec theta cosec theta +2
therefore, L.H.S. = R.H.S.

Hope u will understand the way I solved...._/\_