Prove the identity
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lhs = (sinθ+ cosθ)(sinθ/cosθ + cosθ/sinθ)
=(sinθ+cosθ)(sin^2θ+cos^2θ)/sinθcosθ
=(sinθ+cosθ)/sinθcosθ
=sinθ/sinθcosθ +cosθ/sinθcosθ
=1/cosθ +1/sinθ
=secθ+cosecθ
=rhs
=(sinθ+cosθ)(sin^2θ+cos^2θ)/sinθcosθ
=(sinθ+cosθ)/sinθcosθ
=sinθ/sinθcosθ +cosθ/sinθcosθ
=1/cosθ +1/sinθ
=secθ+cosecθ
=rhs
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