If sin²A-cos²A=1/2 find the value of cos A .

If $\sin^{2}A-\cos^{2}A=\frac{1}{2}$ find the value of $\cos A$ .

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Correct answer: C

Explanation

The correct answer is option 3 i.e. $1\over2$ .

Given, $\sin^{2}A-\cos^{2}A=\frac{1}{2}$ ...(i)

Also, sin²A + cos²A = 1 ...(ii)

Now, subtract equation (i) from equation (ii),

⇒ 2cos²A = 1/2

⇒ cos²A = 1/4

⇒ cos A = 1/2

SSC CGL 2025 PYQ — Question 52