Question

prove that sinθ(1+tanθ)+cosθ(1+cotθ)=secθ+cosecθ

Answer 1

thita =A
L.H.S=sin A (1+sin A/cos A)+cos A (1+cos A/sin A)
=sin A (cos A+sinA /cos A /cos A )+cos A (sin A +cos A /sin A )
=sin ^2A (cosA+sin A)+cos ^2A (sin A+cos A )/cos A sinA
= (sin ^2A+cos ^2A)×(sin A+cos A)/cos A sin A
=sin A/cosA sin A+cosA /cos A sin A (sin ^2A+cos ^2A=1)
=1/cosA +1/sin A
=sec A+cosec A=R.H.S

Answer 2

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