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If cos⁻¹x + cos⁻¹y = (2π)/(7), then sin⁻¹x + sin⁻¹y equals

1. (4π)/(7)
2. (3π)/(7)
3. (2π)/(7)
4. (5π)/(7)

Correct answer: (5π)/(7)

Solution

Since sin^-1 t + cos^-1 t = pi/2 for each variable, sin^-1 x + sin^-1 y = pi - (cos^-1 x + cos^-1 y) = pi - 2pi/7 = 5pi/7.

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