Trigonometry

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 $$sin\left( { 45 }^{ \circ  }+\theta  \right) -cos\left( { 45 }^{ \circ  }-\theta  \right) $$.