If sin²A+cos²A=1 and tanA=2, find sinA and cosA.

Correct Answer is : sinA=25{2}{{5}}52, cosA=15{1}{{5}}51

Correct Answer is : sinA=25{2}{{5}}52, cosA=15{1}{{5}}51

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SSC CHSL 14 Nov 2025 Shift 2 Paper

Question : 73 of 100

Marks: +1, -0

sin^{2}A+cos^{2}A=1

and tanA=2, find sinA and cosA.

Solution:

Concept:

Use the relation

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

and the identity

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

to find both values.

Explanation:

Given

\tan A = 2

, so

\frac{\sin A}{\cos A} = 2

. This gives

\sin A = 2 \cos A

Substitute into

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

(2\cos A)^2 + \cos^2 A = 1

Simplify:

4\cos^2 A + \cos^2 A = 5\cos^2 A = 1

. Thus

\cos^2 A = \frac{1}{5}

Take the positive root (since

\tan A

is positive):

\cos A = \frac{1}{\sqrt{5}}

Then

\sin A = 2 \cos A = 2 \times \frac{1}{\sqrt{5}} = \frac{2}{\sqrt{5}}

Answer:

Option A:

\sin A = \frac{2}{\sqrt{5}}

\cos A = \frac{1}{\sqrt{5}}

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