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SSC CGL Tier I 12 Sep 2025 Shift 2 Paper

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Question : 75 of 100

Marks: +1, -0

If secA = (13)/(5)and A is acute, find sinA

$(5)/(13)$
$(12)/(13)$
$(13)/(12)$
$(13)/(5)$

Solution:

Concept:

Use the reciprocal identity

\sec A = 1/\cos A

and the Pythagorean identity

\sin^2 A + \cos^2 A = 1

.

Explanation:

Given

\sec A = 13/5

. Since

\sec A = 1/\cos A

, we have

\cos A = 5/13

.

Now,

\sin^2 A = 1 - \cos^2 A = 1 - (5/13)^2 = 1 - 25/169 = 144/169

.

Taking square root,

\sin A = \pm 12/13

. Because angle

A

is acute (between

0^\circ

and

90^\circ

), sine is positive. Hence

\sin A = 12/13

.

Answer:

\frac{12}{13}

(Option B)

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