### Trigonometry

goals
If $\dfrac{\pi}{2}<\theta <\pi$ the possible answers  of $\sqrt { 2+\sqrt { 2+2\cos { \theta } } }$ is/are:
In triangle abc and triangle xyz, if angle A and angle Z are acute angles such that Cos A equal to cos x then show that angle A is equal to angle x
Given that $3\sin \theta + 4\cos \theta = 5\,where\,\theta \in \left( {0,{\pi \over 2}} \right).$ Find the value of $2\sin \theta + \cos \theta + 4\tan \theta + 3\cot \theta$
If $\sin{\theta}=n\sin{(\theta+2\alpha)}$, then $\tan{(\theta+\alpha)}$ is equal to
Write the value of $sin\left( { 45 }^{ \circ }+\theta \right) -cos\left( { 45 }^{ \circ }-\theta \right)$.