SSC CHSL 2022 PYQ — Question 73

The correct answer is option 1 i.e.  $\frac{\sqrt{10+2\sqrt{5}}}{4}$

Given:

sin 18^∘ = $\frac{\sqrt{5}-1}{4}$

Concept Used:

$sin^2 \theta + cos^2 \theta = 1$   ....(i)

Explanation:

From equation (i), we get

sin²18° + cos²18° = 1

⇒ cos²18° = 1 - sin²18°

⇒ cos²18° = 1 - ( $\frac{\sqrt{5}-1}{4}$ )²

⇒ cos²18° = 1 - $6 - 2\sqrt{5} \over 16$

⇒ cos²18° = $\frac{{10+2\sqrt{5}}}{16}$

Taking square root on both sides, we get

cos18° = $\frac{\sqrt{10+2\sqrt{5}}}{4}$

Hence the required answer is $\frac{\sqrt{10+2\sqrt{5}}}{4}$ .