Question

1.2.

Answer 1

Answer:

The identity is proved below.

Step-by-step explanation:

The tangent of an angle $\theta$ is given by:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

In this question, we are given the following trigonometric identity:

$\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\tan{\theta}}{1+\tan{\theta}}$

Applying the tangent

$\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{1+\frac{\sin{\theta}}{\cos{\theta}}}$

Now, we apply the least common multiple on the denominator. So

$\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{\frac{\cos{\theta}+\sin{\theta}}{\cos{\theta}}}$

SImplifying the cosine:

$\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}}$

Which means that the identity is proved.