Prove thtcostheta sintheta - sinthetacos[90 - theta ] costheta/ sec [90 - theta ] - costhetasin[90 - theta ] sintheta / cosec[90 - theta] + cosec[90 - theta = 1/ costheta
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cosθsinθ - sinθcos(90°-θ)cosθ/sec(90°-θ) - cosθsin(90°-θ)sinθ/cosec(90°-θ) +cosec(90°-θ)
=cosθsinθ - sinθsinθcosθ/cosecθ - cosθcosθsinθ/secθ - secθ
=cosθsinθ - sin³θcosθ- cos³θsinθ- secθ
=cosθsinθ(1-sin²θ - cos²θ) - secθ
=cosθsinθ(1-1) - secθ
=0 - secθ
=1/cosθ = RHS
=cosθsinθ - sinθsinθcosθ/cosecθ - cosθcosθsinθ/secθ - secθ
=cosθsinθ - sin³θcosθ- cos³θsinθ- secθ
=cosθsinθ(1-sin²θ - cos²θ) - secθ
=cosθsinθ(1-1) - secθ
=0 - secθ
=1/cosθ = RHS
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