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If sin⁻¹(x/5) + cosec⁻¹(5/4) = π/2, then what is the value of x?

1. 4
2. 5
3. 1
4. 3

Correct answer: 3

Solution

The equation states that the sum of the inverse sine of x/5 and the inverse cosecant of 5/4 equals π/2. This implies that sin⁻¹(x/5) is the complementary angle to cosec⁻¹(5/4), which means sin⁻¹(x/5) = π/2 - cosec⁻¹(5/4). Since cosec⁻¹(5/4) corresponds to sin(θ) = 4/5, we find that x/5 must equal 3/5, leading to x = 3.

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