Question

The value of cos^(-1)sqrt(2/3)-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A) pi/3 (B) pi/4 (C) pi/2 (D) pi/6​

Answer 1

Answer:

d) pi / 6 is your answer

Step-by-step explanation:

⇒ $tan^{-1}$ ( $\frac{1}{\sqrt{2} }$ )  -  $tan^{-1}$  $( \frac{\sqrt{3}-\sqrt{2} }{1+\sqrt{6} } )$

⇒ $tan^{-1} \frac{1}{\sqrt{2} }$   -  {  $tan^-\sqrt{3}}$  -  $tan^-\sqrt{2}}$  }

taking  $tan^-\sqrt{3}}$  outside bracket

⇒ (  $tan^{-1}$  $\frac{1}{\sqrt{2} }$  + $tan^-\sqrt{2}}$ )  -  $tan^-\sqrt{3}}$

$\frac{pi}{2}$ × $\frac{pi}{3}$ = $\frac{pi}{6}$

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