Perform each indicated operation and simplify the result so that there are no quotients.
cos x/sec x + sin x/csc x

Guida verificata passo dopo passo

Recall the definitions of the reciprocal trigonometric functions: \(\sec x = \frac{1}{\cos x}\) and \(\csc x = \frac{1}{\sin x}\).

Rewrite each quotient using these definitions: \(\frac{\cos x}{\sec x} = \cos x \times \cos x\) and \(\frac{\sin x}{\csc x} = \sin x \times \sin x\).

Simplify the expressions by multiplying: \(\cos x \times \cos x = \cos^{2} x\) and \(\sin x \times \sin x = \sin^{2} x\).

Add the two simplified terms together: \(\cos^{2} x + \sin^{2} x\).

Use the Pythagorean identity \(\sin^{2} x + \cos^{2} x = 1\) to simplify the expression to its simplest form.

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Reciprocal identities relate trigonometric functions to their reciprocals, such as sec x = 1/cos x and csc x = 1/sin x. Understanding these allows you to rewrite expressions like cos x/sec x and sin x/csc x without fractions.

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