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MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If log⁡x=−13\log x = \frac{-1}{3} , log⁡y=25\log y = \frac{2}{5} and P=log⁡(sin⁡(arccos⁡1−x2))P = \log (\sin(\arccos \sqrt{1-x^2})) , Q=log⁡(cos⁡(arctan⁡1−x2y2xy))Q = \log \left( \cos \left( \arctan \frac{\sqrt{1-x^2 y^2}}{xy} \right) \right) , then (1) P=−19P = \frac{-1}{9} (2) P+Q=−415P + Q = \frac{-4}{15} (3) P−Q=−25P - Q = \frac{-2}{5} (4) PQ=−5\frac{P}{Q} = -5

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