Question

What basic trigonometric identity would you use to verify that sin^2x +cos^2x/cos x = sec x

Answer 1

C

Explanation:

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Answer 2

The basic identity used is
`\bold{\sin ^(2) x+\cos ^(2) x=1}`.

Solution:

In this problem some of the basic trigonometric identities are used to prove the given expression.

Let’s first take the LHS:

`\Rightarrow (\sin ^(2) x+\cos ^(2) x)/(\cos x)`

Step one:

The sum of squares of Sine and Cosine is 1 which is:

`\sin ^(2) x+\cos ^(2) x=1`

On substituting the above identity in the given expression, we get,

`\Rightarrow (\sin ^(2) x+\cos ^(2) x)/(\cos x)=(1)/(\cos x) \rightarrow(1)`

Step two:

The reciprocal of cosine is secant which is:

`\cos x=(1)/(\sec x)`

On substituting the above identity in equation (1), we get,

`\Rightarrow (\sin ^(2) x+\cos ^(2) x)/(\cos x)=\sec x`

Thus, RHS is obtained.

Using the identity
`\sin ^(2) x+\cos ^(2) x=1`, the given expression is verified.