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Maths Trigonometrical Ratios, Functions and Identities General Subjective Type

Published on: August 12, 2026

Solve the equation sin x – cos x = cos 2 x.

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

x = (2n + 1) π : n ∈ Ι , x = 2n π ± , n ∈ Ι

sin x = 2(cos x + cos 2 x)

Squaring both sides, we get

3 sin 2 x = 4(cos 2 x + cos 4 x + 2 cos3x)

⇒ 3(1 – cos 2 x) = 4 cos 2 x + 4 cos 4 x + 8 cos3x.

⇒ 4 cos 4 x + 8 cos 3 x + 7 cos 2 x – 3 = 0

⇒ (cos x + 1) (2 cos x – 1) (2 cos 2 x + 3 cos x + 3) = 0

⇒ cos x = – 1 ⇒ x = (2n + 1) π : n ∈ Ι

or cos x = ⇒ x = 2n π ± , n ∈ Ι

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