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Question: The value of \(\cos ^ { - 1 } \left( - \frac { 1 } { 2 } \right) - 2 \sin ^ { - 1 } \left( \frac {...

The value of

cos⁡−1(−12)−2sin⁡−1(12)+3cos⁡−1(−12)−4tan⁡−1(−1)\cos ^ { - 1 } \left( - \frac { 1 } { 2 } \right) - 2 \sin ^ { - 1 } \left( \frac { 1 } { 2 } \right) + 3 \cos ^ { - 1 } \left( - \frac { 1 } { \sqrt { 2 } } \right) - 4 \tan ^ { - 1 } ( - 1 )

is equal to

A

7π/4

B

11π/4

C

π/12

D

25π/12

Answer

25π/12

Explanation

Solution

We have cos⁡−1(−12)−sin⁡−1(12)+3cos⁡−1(−12)\cos^{- 1}\left( - \frac{1}{2} \right) - \sin^{- 1}\left( \frac{1}{2} \right) + 3\cos^{- 1}\left( - \frac{1}{\sqrt{2}} \right)-4tan⁡−1(−1)4\tan^{- 1}( - 1)

= 2π3−2 x π6+3 x 3π4−4(−π4)=25π12\frac{2\pi}{3} - 2\text{ x }\frac{\pi}{6} + 3\text{ x }\frac{3\pi}{4} - 4\left( - \frac{\pi}{4} \right) = \frac{25\pi}{12}