JEE Main202431 Jan 2024Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If a = sin − 1 sin 5 and b = cos − 1 cos 5 , then a 2 + b 2 is equal to

Options

A4 π 2 + 25
B8 π 2 − 40 π + 50
C4 π 2 − 20 π + 50
D25

Correct answer

B. 8 π 2 − 40 π + 50

Step-by-step solution

Given: a = sin - 1 sin 5 and b = cos - 1 cos 5 ⇒ a = 5 - 2 π and b = 2 π - 5 ⇒ a 2 + b 2 = 5 - 2 π 2 + 2 π - 5 2 ⇒ a 2 + b 2 = 25 + 4 π 2 - 20 π + 4 π 2 + 25 - 20 π ⇒ a 2 + b 2 = 8 π 2 - 40 π + 50

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