Question

sec(90-theta)sin(90-theta)+cosec(90-theta)cos(90-theta) =sec theta cosec theta

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Answer 1

hello.................................

L.H.S

sec[90-Ф].sin[90-Ф]+cosec[90-Ф].cos[90-Ф]
cosecФ.cosФ+secФ.sinФ
cosФ/sinФ+sinФ/cosФ
cos²Ф+sin²Ф/[sinФ.cosФ]
1/[sinФ.cosФ]
secФ.cosecФ=R.H.S

hence proved

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hope this would help you
@Rohit

Answer 2

LHS.= cosec theta × cos theta + sec theta × sin theta
= 1/ sin theta × cos theta + 1/ cos theta × sin theta
= cos theta/ sin theta + sin theta / cos theta
= cos ^2theta + sin ^ 2 theta / sin theta × cos theta
= 1/ sin theta × 1 / cos theta
= cosec theta × sec theta
= RHS
Proved..