Trigonometric Functions of Sum and Difference of Two Angles

$\int \frac{\sin x}{1-\sin x}dx=$

Period of $\sin \theta -\sqrt{3}\cos \theta$ is

$\cos \alpha =\frac{-4}{5}$ and $\sin \alpha =\frac{-3}{5}$ then find $\frac{\sin 1500⁰+2\cos 1350⁰}{\tan \alpha }$

If $∆\mathrm{ABC},$ prove that ${\sin }^2\mathrm{A}+{\sin }^2\mathrm{B}-{\sin }^2\mathrm{C}=2\mathrm{sinA} \mathrm{sinB} \mathrm{sinC}$

If $\cos x+\cos y=p, \sin x+\sin y=q, \text{then} \cos \left(\frac{x-y}{2}\right)=$

If $\cos x+\cos y=p, \sin x+\sin y=q, \text{then} \cos \left(\frac{x-y}{2}\right)=$

If $y={\cos }^{-1}x, -1⩽x⩽1,0⩽y⩽\mathrm{\pi }$ then prove that $\frac{dy}{dx}=-\frac{1}{\sqrt{1-x^2}}.$

$\frac{{\sin }^2{\displaystyle \frac{\mathrm{\pi }}{18}}{\displaystyle +}{\displaystyle {\sin }^2}{\displaystyle \frac{{\displaystyle \mathrm{\pi }}}{{\displaystyle 9}}}{\displaystyle +}{\displaystyle {\sin }^2}{\displaystyle \frac{{\displaystyle 7\mathrm{\pi }}}{{\displaystyle 18}}}{\displaystyle +}{\displaystyle {\sin }^2}{\displaystyle \frac{{\displaystyle 4\mathrm{\pi }}}{{\displaystyle 18}}}}{{\cos }^2\frac{\mathrm{\pi }}{18}+{\cos }^2\frac{{\displaystyle \mathrm{\pi }}}{{\displaystyle 9}}+{\cos }^2\frac{{\displaystyle 7\mathrm{\pi }}}{{\displaystyle 18}}+{\cos }^2\frac{{\displaystyle 4\mathrm{\pi }}}{{\displaystyle 18}}}=$

Evaluate$\int \left({\sin }^{2}x+{\cos }^{2}x\right)dx$

If $\mathrm{\pi }<\theta <2\mathrm{\pi }$ then $\frac{1}{\sin \theta -\sqrt{{\cot }^2\theta -{\cos }^2\theta }}=$

If ${\cos }^{2}x+\sin x+1=0$ then the value of $x$ lies in the interval $?$

If $\sec \alpha =\frac{-13}{5} \& \cot \beta =\frac{-15}{8}$ where $\alpha \in \left(\frac{\mathrm{\pi }}{2},\mathrm{\pi }\right), \beta \in \left(\frac{3\mathrm{\pi }}{2},2\mathrm{\pi }\right).$ Find $\cos \left(\alpha -\beta \right).$

Evaluate $\int \frac{dx}{1-\tan x}$

Evaluate: $\int \frac{dx}{{\sin }^{2}x.{\cos }^{2}x}$

${\int }_0^{3\mathrm{\pi }}\frac{e^{\cos x}}{\left(1+{\cos }^{2}x\right)\left(e^{\cos x}+e^{-\cos x}\right)}dx$

Prove that $\frac{\cos A\cos C+\cos \left(A+B\right)\cos \left(B+C\right)}{\cos A\sin C-\sin \left(A+B\right)\cos \left(B+C\right)}=\cot C$

Prove that ${\int }_0^{\frac{\mathrm{\pi }}{2}}\log \left(\tan x\right)dx=0$

Evaluate $\frac{\sin {84}^{\circ }-\sin 6^{\circ }}{\sin {84}^{\circ }+\sin 6^{\circ }}$