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What is cos ^275^°-sin ^215^° equal to? Single correct option
What is
cos 2 75 ∘ − sin 2 15 ∘ \cos^275^\circ-\sin^215^\circ cos 2 7 5 ∘ − sin 2 1 5 ∘ equal to?
A. 1 2 \dfrac12 2 1 B. 3 2 \dfrac{\sqrt3}{2} 2 3 C. 0 0 0 D. − 1 2 -\dfrac12 − 2 1 Show answer and solution Answer: (C) 0 0 0
Since
sin 15 ∘ = cos ( 90 ∘ − 15 ∘ ) = cos 75 ∘ \sin15^\circ=\cos(90^\circ-15^\circ)=\cos75^\circ sin 1 5 ∘ = cos ( 9 0 ∘ − 1 5 ∘ ) = cos 7 5 ∘ , the two terms are equal and the difference is
0 0 0 . Trap: applying
cos 2 A − sin 2 A = cos 2 A \cos^2A-\sin^2A=\cos2A cos 2 A − sin 2 A = cos 2 A with unequal angles gives
cos 150 ∘ \cos150^\circ cos 15 0 ∘ -type values.
Original question written in the NDA 2024 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