Prove that $cos e c to the power of negative 1 end exponent x plus s e c to the power of negative 1 end exponent x equals straight pi over 2 comma space open vertical bar x close vertical bar greater or equal than 1$

Solution

$Let space cosec to the power of negative 1 end exponent straight x equals straight theta space space space space space space space space space space space space space space rightwards double arrow space space straight x equals sec open parentheses straight pi over 2 minus straight theta close parentheses rightwards double arrow space space space sec to the power of negative 1 end exponent straight x equals straight pi over 2 minus straight theta space space space space space space space space rightwards double arrow space sec to the power of negative 1 end exponent straight x equals straight pi over 2 minus cosec to the power of negative 1 end exponent straight x rightwards double arrow space space space sec to the power of negative 1 end exponent straight x plus cosec to the power of negative 1 end exponent straight x equals straight pi over 2$

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Inverse Trigonometric Functions

Prove that $cos e c to the power of negative 1 end exponent x plus s e c to the power of negative 1 end exponent x equals straight pi over 2 comma space open vertical bar x close vertical bar greater or equal than 1$

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