Q10 of 104 Page 204

Prove the following by using trigonometric identities:

(sinθ — secθ)2 + (cosθ — cosecθ)2 = (1 — secθ ⋅ cosecθ)2.

L.H.S


= sin2θ – 2sinθsecθ + sec2θ + cos2θ – 2cosθcosecθ + cosec2θ


= (sin2θ + cos2θ) – (2sinθsecθ + 2cosθcosecθ) + cosec2θ + sec2θ







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