Evaluating the Trigonometric expressions in functions by simplification Questions with solutions

The trigonometry problems on simplifying the trigonometric functions based expressions for your practice with examples, and worksheet on evaluating the trigonometric expressions in which the trigonometric functions are involved and also solutions to learn how to evaluate the trigonometric expressions in trigonometric functions by simplification using the trigonometric identities.

Evaluate $\sin{x}\tan{x}$ $+$ $\cos{x}$

Evaluate $(\sec{x}+\tan{x})$ $\bigg(\dfrac{1-\sin{x}}{\cos{x}}\bigg)$

Evaluate $\dfrac{1+\sin{x}}{\cos{x}}$ $+$ $\dfrac{\cos{x}}{1+\sin{x}}$

Evaluate $\sin{(x+60^\circ)}$ $-$ $\cos{(x+30^\circ)}$

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