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The value of sin ^225^°+sin ^265^° is Single correct option
The value of
sin 2 25 ∘ + sin 2 65 ∘ \sin^225^\circ+\sin^265^\circ sin 2 2 5 ∘ + sin 2 6 5 ∘ is
A. 0 0 0 B. 1 2 \dfrac12 2 1 C. 1 1 1 D. 2 2 2 Show answer and solution Answer: (C) 1 1 1
Since
65 ∘ = 90 ∘ − 25 ∘ 65^\circ=90^\circ-25^\circ 6 5 ∘ = 9 0 ∘ − 2 5 ∘ ,
sin 65 ∘ = cos 25 ∘ \sin65^\circ=\cos25^\circ sin 6 5 ∘ = cos 2 5 ∘ . So the expression is
sin 2 25 ∘ + cos 2 25 ∘ = 1 \sin^225^\circ+\cos^225^\circ=1 sin 2 2 5 ∘ + cos 2 2 5 ∘ = 1 . Treating the angles as supplementary rather than complementary would lead to wrong values.
Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake