The sum of two angles is $135°$, and their difference is $\frac{\mathrm{\pi }}{12}$, find the value of the angles in degree and in circular measure.

In a quadrilateral, the three angles are $\frac{\mathrm{\pi }}{3}, \frac{5\mathrm{\pi }}{6}$ and $90°$, find the fourth angle in circular measure.

If the angle of a parallelogram is $67°30\text{'}$, find the circular measure of the other three angles.

If $\alpha$ is a positive acute angle and $\sin \alpha =\frac{5}{13}$ then, show that $\tan \alpha +\sec \alpha =\frac{3}{2}$

If $\tan \theta =\frac{3}{4}$ then, find the value of $\left({\cos }^2 \theta -{\sin }^2 \theta \right)$.

If $\tan \theta =\frac{5}{12}$ then, show that $\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}=\frac{1}{5}$.

If in an isosceles triangle $\mathrm{ABC}, \mathrm{AB}=\mathrm{AC}=10 \mathrm{cm}$, and $\mathrm{BC}=12 \mathrm{cm}$, then find the value of $\mathrm{cosec} \mathrm{B}+\cot \mathrm{C}$

In triangle $\mathrm{ABC}, \angle \mathrm{A}=90°$. If $\mathrm{BC}=2\sqrt{5} \mathrm{cm}$ and $\mathrm{AB}+\mathrm{AC}=6 \mathrm{cm}$, then find the value of $\sin \mathrm{B}+\sin \mathrm{C}$.