In the right-angled triangle, ABC, ∠ B = 90° and angle A and angle C are acute angles. If cosecA = 2√(2) , then find the value of sinA . cosC + cosA . sinC.

In the right-angled triangle, ABC, ∠ B = 90° and angle A…

In the right-angled triangle, ABC, $\angle$ B = 90° and angle A and angle C are acute angles. If cosecA = $2\sqrt{2}$ , then find the value of sinA . cosC + cosA . sinC.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 1.

In Triangle △ABC, ∠B = 90°.

∠B = 90°, we have ∠A + ∠C = 90°

We know that

sin(A + B) = sinA.cosB + cosA.sinB

So,

⇒ sinA.cosC + cosA.sinC = sin(A + C)

= sin(90°)

= 1

SSC CHSL 2024 PYQ — Question 73