Triggy

Geometry Level 2

sec ⁡ ( π 2 − x ) sec ⁡ x \large \dfrac{\sec{\left ( \frac{\pi}{2}-x \right )}}{\sec x}

Which of the following trigonometric functions is equivalent to the expression above?

1 1 sec ⁡ x \sec x cot ⁡ x \cot x sin ⁡ x \sin x 1 2 sin ⁡ 2 x \dfrac{1}{2} \sin 2x None of these

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Michael Fuller by Michael Fuller , 22, United Kingdom

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1 solution

Michael Fuller
Feb 26, 2016

sec ⁡ ( π 2 − x ) sec ⁡ x = cos ⁡ x cos ⁡ ( π 2 − x ) = cos ⁡ x sin ⁡ x = cot ⁡ x \dfrac{\sec{\left ( \dfrac{\pi}{2}-x \right )}}{\sec x} =\dfrac{\cos x}{\cos{\left ( \dfrac{\pi}{2}-x \right )}} =\dfrac{\cos x}{\sin x} = \large \color{#20A900}{\boxed{\cot x}}

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