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Ivenika [448]
3 years ago
15

Verify the identity

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0

<u>Given</u>:

Given that we need to prove the identity \sin x+\sin x \tan ^{2} x=\tan x \sec x

<u>Proof</u>:

Step 1: Factor out the common term sin x, we get;

\sin x\left(1+\tan ^{2} x\right)=tan \ x \ sec \ x

Step 2: Using the identity 1+tan^2 x=sec^2x

\sin x \sec ^{2} x=tan \ x \ sec \ x

Step 3: Reciprocating sec x, we get;

\sin x \cdot \frac{1}{\cos ^{2} x}=tan \ x \ sec \ x

Step 4: Splitting the denominator, we have;

\frac{\sin x}{\cos x} \cdot \frac{1}{\cos x}=tan \ x \ sec \ x

Simplifying, we get;

\tan x \sec x=\tan x \sec x

Thus, the identity is proved.

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