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Question: If A = 2 tan<sup>–1</sup>\((2\sqrt{2} - 1)\) and B=3sin<sup>–1</sup>\(\frac{1}{3}\)+ sin<sup>–1</su...

If A = 2 tan–1(22−1)(2\sqrt{2} - 1) and

B=3sin–113\frac{1}{3}+ sin–135\frac{3}{5}, then

A

B < A < 1050

B

1050< B < A

C

B < 1050< A

D

1050< A < B

Answer

B < 1050< A

Explanation

Solution

A = 2tan–1(222\sqrt{2} – 1) > 2 tan–13\sqrt{3} = 1200

B = 3tan–1122\frac{1}{2\sqrt{2}} + cos–145\frac{4}{5} < 3tan–1(2−1)(\sqrt{2} - 1) + cos–15+14\frac{\sqrt{5} + 1}{4}

= 10312103\frac{1}{2}