Consider a triangle PQR, right-angled at R, in which PQ =…

Consider a triangle PQR, right-angled at R, in which PQ = 29 unit, QR = 21 unit, and ∠PQR = θ. Find the value of cos⁡²θ − sin⁡²θ.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. $41\over841$ .

Using Pythagoras' theorem, we get

PR² = PQ² - QR²

⇒ PR² = 29² - 21²

⇒ PR² = 841 - 441 = 400

⇒ PR = 20

Now,

cos²θ = 21²/29² = 441/841

sin²θ = 20²/29² = 400/841

Hence,

⇒ cos²θ − sin²θ = (441/841) - (400/841) = 41/841

SSC CGL 2024 PYQ — Question 55