1.

Prove that :sin θ .cos (90° - θ) + cos θ sin (90° - θ).

Answer»

Taking LHS = sin θ cos (90° - θ) + cos θ sin (90° - θ)

⇒ sin θ × sin θ + cos θ × cos θ [∵ Sin θ = cos (90° - θ) and cos θ = sin (90° - θ) ]

⇒ cos2 θ + sin2 θ [∵ cos2 θ + sin2 θ = 1]

= 1 = RHS

Hence Proved



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