Q3 of 80 Page 311

If sin θ + cos θ = 1, then let us determine the value of sin θ × cos θ.

Given, sinθ + cosθ = 1


⇒ squaring on both sides


⇒ (sinθ + cosθ)2 = 12


⇒ sin2θ + cos2θ + 2sinθcosθ = 1


⇒ 1 + 2sinθ cosθ = 1


⇒ 2sinθ cosθ = 0


⇒ sinθ × cosθ = 0


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