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Question 1:

In the given figure, if $\mathrm{AB}=\mathrm{AC}=8 \mathrm{~cm}, \mathrm{BC}=$ $11 \mathrm{~cm}$ and $\mathrm{BD}=7 \mathrm{~cm}$, then find $\mathrm{AD}=$ ?

Question 2:

The equation $\cos 2 \theta+p \sin \theta=2 p-7$ has a solution

Question 3:

If $\alpha+\beta+\gamma=\alpha \beta \gamma$ ,then value of $\frac{\alpha}{1-\alpha^{2}} + \frac{\beta}{1-\beta^{2}}+\frac{\gamma}{1-\gamma^{2}}$ is

Question 4:

The maximum value of $\sin x+\cos x$ is:

Question 5:

Find the value $\cos ^{4}\left(\frac{\pi}{8}\right)+\cos ^{4}\left(\frac{3 \pi}{8}\right)+\cos ^{4}$ $\left(\frac{5 \pi}{8}\right)+\cos ^{4}\left(\frac{7 \pi}{8}\right)$

Question 6:

Find the value $\tan 2 x$.

Question 7:

If $(\sec \alpha+\tan \alpha)(\sec \beta+\tan \beta)(\sec \gamma+\tan \gamma)$ $=\tan \alpha\tan \beta \tan \gamma$, find the value of $(\sec \alpha-$ $\tan \alpha)(\sec \beta-\tan \beta)(\sec \gamma-\tan \gamma)$

Question 8:

$\frac{\sin A+\sin B}{\cos A-\cos B}+\frac{\cos A+\cos B}{\sin A-\sin B}=?$

Question 9:

If $\sec A=\frac{41}{40}$, given that $A<90^{\circ}$, What is the value of the following? 

$\frac{82 \sin A+9 \cot A}{164 \cos A-80 \tan A}$

Question 10:

If $3\left(\sec ^2 \theta+\tan ^2 \theta\right)=5,0^{\circ}<\theta<90^{\circ}$, then the value of $\operatorname{cosec} \theta$ is: