Math Doubts

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

The addition of cosine of angle $x$ minus cosine of three times angle $x$ divided by cosine of angle $x$ and sine of angle $x$ plus sine of three times angle $x$ divided by sine of angle $x$ is a trigonometric expression in this trigonometry problem.

There are two different mathematical methods to find the value of the given multiple angle trigonometric expression. So, let’s learn each method with understandable steps to know how to calculate the value of the given triple angle trigonometric expression.

Triple angle identities

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

Learn how to find the $\cos{x}$ minus $\cos{3x}$ divided by $\cos{x}$ plus $\sin{x}$ plus $\sin{3x}$ divided by $\sin{x}$ by the expansion of sine and cosine triple angle trigonometric identities.

Solution

Sum & Difference to Product identities

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

Learn how to calculate the value of $\cos{x}$ minus $\cos{3x}$ divided by $\cos{x}$ plus $\sin{x}$ plus $\sin{3x}$ divided by $\sin{x}$ by the sum and difference to product transformation trigonometric identities.

Solution