Considering only the principal values of the inverse trigonometric functions, the value of $\frac{3}{2} \cos^{- 1} \sqrt{\frac{2}{2 + π^{2}}} + \frac{1}{4} \sin^{- 1} \frac{2 \sqrt{2} π}{2 + π^{2}} + \tan^{- 1} \frac{\sqrt{2}}{π}$ is _______.
(If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places)

Question

Considering only the principal values of the inverse trigonometric functions, the value of $\frac{3}{2} \cos^{- 1} \sqrt{\frac{2}{2 + π^{2}}} + \frac{1}{4} \sin^{- 1} \frac{2 \sqrt{2} π}{2 + π^{2}} + \tan^{- 1} \frac{\sqrt{2}}{π}$ is _______.

(If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places)

Aicharya · Accepted Answer

3 2 cos - 1 2 2 + &#960; 2 + 1 4 sin - 1 2 2 &#960; 2 + &#960; 2 + tan - 1 2 &#960; = 3 2 tan - 1 &#960; 2 + 1 4 tan - 1 2 2 &#960; &#960; 2 - 2 + tan - 1 2 &#960; = &#960; 2 + 1 2 tan - 1 &#960; 2 - 1 4 tan - 1 2 2 &#960; 2 - &#960; 2 = &#960; 2 + 1 2 tan - 1 &#960; 2 - 1 4 tan - 1 2 &#183; &#960; 2 1 - &#960; 2 2 = &#960; 2 + 1 2 tan - 1 &#960; 2 - 1 4 - &#960; + 2 tan - 1 &#960; 2 = &#960; 2 + &#960; 4 = 3 &#960; 4 = 2 . 36

Considering only the principal values of the inverse trigonometric functions, the value of 3 2 cos - 1 2 2 +…

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