The expression sin -1((1/√2))+ sec -1(-√2)+ tan -1(-1)+ operatornamecosec-1(-√2)+ cos -1(-(1/2))+ tan -1(1-√2)+ cot -1(√2+1) simplifies to

Question

The expression sin -1((1/√2))+ sec -1(-√2)+ tan -1(-1)+ operatornamecosec-1(-√2)+ cos -1(-(1/2))+ tan -1(1-√2)+ cot -1(√2+1) simplifies to (A) π (B)  (7 π/6) (C) 0 (D) (π/2)

Tardigrade Admin · Accepted Answer

(π/4)+(3 π/4)-(π/4)-(π/4)+(2 π/3)-(π/8)+(π/8)=(7 π/6)

Q. The expression $sin^{- 1} (\frac{1}{2}) + sec^{- 1} (- 2) + tan^{- 1} (- 1) + cosec^{- 1} (- 2) + cos^{- 1} (- \frac{1}{2}) + tan^{- 1} (1 - 2) + cot^{- 1} (2 + 1)$ simplifies to

$π$

$\frac{7 π}{6}$

0

$\frac{π}{2}$

$\frac{π}{4} + \frac{3 π}{4} - \frac{π}{4} - \frac{π}{4} + \frac{2 π}{3} - \frac{π}{8} + \frac{π}{8} = \frac{7 π}{6}$

Q. The expression sin−1(2​1​)+sec−1(−2​)+tan−1(−1)+cosec−1(−2​)+cos−1(−21​)+tan−1(1−2​)+cot−1(2​+1) simplifies to

π

67π​

0

2π​

4π​+43π​−4π​−4π​+32π​−8π​+8π​=67π​

Q. The expression $sin^{- 1} (\frac{1}{2}) + sec^{- 1} (- 2) + tan^{- 1} (- 1) + cosec^{- 1} (- 2) + cos^{- 1} (- \frac{1}{2}) + tan^{- 1} (1 - 2) + cot^{- 1} (2 + 1)$ simplifies to

$π$

$\frac{7 π}{6}$

$\frac{π}{2}$

$\frac{π}{4} + \frac{3 π}{4} - \frac{π}{4} - \frac{π}{4} + \frac{2 π}{3} - \frac{π}{8} + \frac{π}{8} = \frac{7 π}{6}$