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What is the value of sec ^-12+csc ^-12? Single correct option
What is the value of
sec − 1 2 + csc − 1 2 \sec^{-1}2+\csc^{-1}2 sec − 1 2 + csc − 1 2 ?
A. π 3 \dfrac\pi3 3 π B. π 2 \dfrac\pi2 2 π C. 5 π 6 \dfrac{5\pi}6 6 5 π D. π 6 \dfrac\pi6 6 π Show answer and solution Answer: (B) π 2 \dfrac\pi2 2 π
sec − 1 2 = π 3 \sec^{-1}2=\frac\pi3 sec − 1 2 = 3 π since
cos π 3 = 1 2 \cos\frac\pi3=\frac12 cos 3 π = 2 1 , and
csc − 1 2 = π 6 \csc^{-1}2=\frac\pi6 csc − 1 2 = 6 π since
sin π 6 = 1 2 \sin\frac\pi6=\frac12 sin 6 π = 2 1 . The sum is
π 2 \frac\pi2 2 π ; this also follows from
sec − 1 x + csc − 1 x = π 2 \sec^{-1}x+\csc^{-1}x=\frac\pi2 sec − 1 x + csc − 1 x = 2 π for
∣ x ∣ ≥ 1 |x|\ge1 ∣ x ∣ ≥ 1 . Option
π 3 \frac\pi3 3 π is only the first term.
Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake