If cosA = 12/13, find the values of SinA and CotA.

Correct Answer is : 5135/13135 and 12512/5512

Correct Answer is : 5135/13135 and 12512/5512

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SSC CHSL 14 Nov 2025 Shift 1 Paper

Question : 75 of 100

Marks: +1, -0

If cosA =

\frac{12}{13}

, find the values of SinA and CotA.

Solution:

Concept:

Use the Pythagorean identity

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

to find sine, then

\cot A = \frac{\cos A}{\sin A}

Explanation:

Given

\cos A = \frac{12}{13}

. Square it:

\cos^2 A = \frac{144}{169}

From identity:

\sin^2 A = 1 - \cos^2 A = 1 - \frac{144}{169} = \frac{25}{169}

Take positive square root:

\sin A = \frac{5}{13}

Now

\cot A = \frac{\cos A}{\sin A} = \frac{12/13}{5/13} = \frac{12}{5}

Answer:

\sin A = \frac{5}{13}

and

\cot A = \frac{12}{5}

, which matches option C.

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