यदि `sin theta+cos theta =p` तथा `sec theta + cosec theta =q` हो, तो सिद्ध करो कि `q(p^(2)-1)=2p`

Explanation

`LHS =q (p^(2)-1)`
`impliesLHS=(sec theta+cosec theta){(sec theta + cos theta)^(2)-1}" "` [p तथा q का मान रखने पर]
`impliesLHS =((1)/(cos theta)+(1)/(sin theta )){sin ^(2)theta + cos ^(2)theta+ 2 sin theta cos theta-1}`
`impliesLHS =((sin theta + cos theta)/(cos theta sin theta))(1+2 sin theta cos theta-1)`
`impliesLHS =((sin theta+ cos theta )/(cos theta sin theta ))(2 sin cos theta)`
`impliesLHS=2(sin theta + cos theta) = 2p = RHS`