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cupoosta [38]
3 years ago
10

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

Mathematics
1 answer:
gogolik [260]3 years ago
6 0

<u>Answer:</u>

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

<u>Solution: </u>

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

Let’s first take the LHS:

\Rightarrow \frac{\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 \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\frac{1}{\cos x} \rightarrow(1)

Step two:

The reciprocal of cosine is secant which is:

\cos x=\frac{1}{\sec x}

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

\Rightarrow \frac{\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.

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