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SSC CPO Tier 1 Exam 10 Dec 2025 Shift 1

Section: Quantitative Aptitude

Question : 142 of 200

Marks: +1, -0

If sin

x = cos(2x + 15

°) what is the value of x?

Solution:

Concept:

Use the complementary angle identity to rewrite cosine as sine.

Explanation:

Given:

\sin x = \cos(2x + 15^\circ)

Convert the cosine term:

\cos \theta = \sin(90^\circ - \theta)

\cos(2x + 15^\circ) = \sin(90^\circ - (2x + 15^\circ))

Simplify:

90^\circ - 2x - 15^\circ = 75^\circ - 2x

Thus

\cos(2x + 15^\circ) = \sin(75^\circ - 2x)

Now the equation becomes

\sin x = \sin(75^\circ - 2x)

Equate the angles:

x = 75^\circ - 2x

Solve:

x + 2x = 75^\circ

, so

3x = 75^\circ

Divide by 3:

x = 25^\circ

Answer:

x = 25^\circ

, which corresponds to option C.

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