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प्रश्न
If θ = 30°, verify that: 1 - sin 2θ = (sinθ - cosθ)2
उत्तर
Given: θ = 30°
1 - sin2θ
= 1 - sin2 x 30°
= 1 - sin60°
= `1 - sqrt(3)/(2)`
= `(2 - sqrt(3))/(2)`
(sinθ - cosθ)2
= sin2θ + cos2θ - 2sinθ cosθ
= 1 - 2 x sin30° x cos30
= `1 - 2 xx (1)/(2) xx sqrt(3)/(2)`
= `1 - sqrt(3)/(2)`
= `(2 - sqrt(3))/(2)`
⇒ 1 - sin2θ = (sinθ - cosθ)2.
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