Statement-1: $cosec^{-1}\frac{3}{2}+cos^{-1}\frac{2}{3}-2cot^{-1}\frac{1}{7}-cot^{-1}7 = cot^{-1}7.$ Statement-2: $sin^{-1} x + cos^{-1} x =\frac{\pi}{2}, tan^{-1} x + cot^{-1} x =\frac{\pi}{2},$ $cosec^{-1}x = sin^{-1}\frac{1}{x}, $ and for $ x > 0, cot^{-1}x = tan^{-1}\frac{1}{x}$ |
Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1. Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1. Statement 1 is True, Statement 2 is False. Statement 1 is False, Statement 2 is True. |
Statement 1 is False, Statement 2 is True. |
Statement-2 is true (see theory). Using statement-2, we have $cosec^{-1}\frac{3}{2}+cos^{-1}\frac{2}{3}-2cot^{-1}\frac{1}{7}-cot^{-1}7 $ $= \left(sin^{-1}\frac{2}{3}+cos^{-1}\frac{2}{3}\right) - cot^{-1}\frac{1}{7}-(tan^{-1}7 + cot^{-1}7)$ $= \frac{\pi}{2} - cot^{-1}\frac{1}{7}-\frac{\pi}{2} = - cot^{-1}\frac{1}{7}= - tan^{-1}7$ So, statement-1 is not correct. |