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}\left(\frac{1}{\sqrt{2}}\right)+\sec ^{-1}(-\sqrt{2})+\tan ^{-1}(-1)+\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(-\frac{1}{2}\right)+\tan ^{-1}(1-\sqrt{2})+\cot ^{-1}(\sqrt{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}\left(\frac{1}{\sqrt{2}}\right)+\sec ^{-1}(-\sqrt{2})+\tan ^{-1}(-1)+\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(-\frac{1}{2}\right)+\tan ^{-1}(1-\sqrt{2})+\cot ^{-1}(\sqrt{2}+1) simplifies to

π

67π​

0

2π​

4π​+43π​−4π​−4π​+32π​−8π​+8π​=67π​

$π$

$\frac{7 π}{6}$

$\frac{π}{2}$

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