# Evaluate $\dfrac{\sin{3x}}{\sin{x}}$ $-$ $\dfrac{\cos{3x}}{\cos{x}}$

The value of sine of angle three times $x$ divided by sine of angle $x$ minus cosine of angle three times $x$ divided by cosine of angle $x$ can be obtained in two different methods. So, let’s learn each method with understandable steps.

### Triple angle identities

Find $\dfrac{\sin{3x}}{\sin{x}}$ $-$ $\dfrac{\cos{3x}}{\cos{x}}$

Learn how to evaluate the sine of angle three times angle $x$ divided by sine of angle $x$ minus cosine of three times angle $x$ divided by cosine of angle $x$ by using the triple angle trigonometric identities.

### Without Triple angle identities

Evaluate $\dfrac{\sin{3x}}{\sin{x}}$ $-$ $\dfrac{\cos{3x}}{\cos{x}}$

Learn how to find the sine of angle three times angle $x$ divided by sine of angle $x$ minus cosine of three times angle $x$ divided by cosine of angle $x$ without using the triple angle trigonometric identities.

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