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Inverse Trigonometric Functions

Question

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Prove that $sin to the power of negative 1 end exponent space straight x plus space cos to the power of negative 1 end exponent space straight x equals straight pi over 2$

Solution

Let sin^–1x =θ

therefore space space space space space straight x space equals space sinθ space space space space space space space space space space space space space space space rightwards double arrow space straight x equals cos open parentheses straight pi over 2 minus straight theta close parentheses rightwards double arrow space space space cos to the power of negative 1 space end exponent straight x equals straight pi over 2 minus straight theta space space space space space space space rightwards double arrow space cos to the power of negative 1 end exponent straight x equals straight pi over 2 minus sin to the power of negative 1 end exponent straight x rightwards double arrow space space cos to the power of negative 1 end exponent space straight x plus sin to the power of negative 1 end exponent space straight x space equals space straight pi over 2

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