If sin x = 0.6 and x ∈ (0, π/2), find sin2x + cos2x.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 1.24.
sin x = 0.6
⇒ cos x = √(1 - sin2x) = (1 - 0.62)
= √(1 – 0.36)
= √0.64
= 0.8
sin2x + cos2x
= (2 sin x cos x) + (1 – 2 sin2x)
= (2 × 0.6 × 0.8) + (1 – 2 × 0.36)
= 0.96 + 1 – 0.72
= 1.24