# What is $ \cos x $ times $ \sec x $ ?

Last updated date: 18th Mar 2023

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**Hint**: The trigonometric functions are real functions which relate an angle of a right angled triangle to ratios of two side lengths. This problem contains two trigonometric ratios $ \cos x $ and $ \sec x $ , so we use Standard trigonometric identity, which gives the relation between $ \cos x $ and $ \sec x $ to solve this problem.

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__Complete step-by-step answer__There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent.

These six trigonometric ratios are abbreviated as $ \sin ,\cos ,\tan ,\cos ec,\sec ,\cot $ .

Using these six trigonometric ratios several trigonometric identities can be formed.

Trigonometric identities are equalities that involve trigonometric function and are true for every value of the occurring variables for which both sides of the equality are defined.

Therefore every trigonometric ratio is related to other ratios with the help of identities.

One such identity is $ \sec x = \dfrac{1}{{\cos x}} $ which relate the ratios $ \cos x $ and $ \sec x $ .

In the problem they have asked the product of $ \cos x $ and $ \sec x $ i.e. $ \cos x \times \sec x $

In the place of $ \sec x $ we use the above identity and write it in terms of $ \cos x $ ,

$ \cos x \times \sec x = \cos x \times \dfrac{1}{{\cos x}} $ , cancelling the common factor $ \cos x $ we get $ 1 $ as the answer.

Therefore $ \cos x \times \sec x = 1 $ .

i.e. $ \cos x $ times $ \sec x $ is $ 1 $

**So, the correct answer is “1”.**

**Note**: Knowing standard trigonometric identities helps in solving numerous math problems which contains trigonometric functions. Learn to write each one of the trigonometric ratios in terms of the rest of the five ratios using identities that will help solve the problems faster.

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