Q. In $\Delta PQR$, right-angled at $Q$, $PR+QR=25$cm and $PQ=5$cm. Determine the values of $\sin P,\cos P$ and $\tan P$.

Q. State whether the following are true or false. Justify your answer.
(i) The value of $\tan A$ is always less than $1$.
(ii) $\sec A=\frac{12}{5}$ for some value of angle $A$.
(iii) $\cos A$ is the abbreviation used for the cosecant of angle $A$.
(iv) $\cot A$ is the product of $\cot$ and $A$.
(v) $\sin \theta =\frac{4}{3}$ for some angle $\theta$.

Q. If $\sin A=\frac{3}{4}$, calculate $\cos A$ and $\tan A$.

Q. In triangle $ABC$, right-angled at $B$, if $\tan A=\frac{1}{\sqrt{3}}$, find the value of:
(i) $\sin A\cos C+\cos A\sin C$
(ii) $\cos A\cos C-\sin A\sin C$

Q. If $\tan 2A=\cot (A-{18}^{\circ })$, where $2A$ is an acute angle, find the value of $A$.

Q. Choose the correct option and justify your choice:
$\sin 2A=2\sin A$ is true when $A=$

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. Choose the correct option and justify your choice:
$\frac{2\tan {30}^{\circ }}{1+{\tan }^2{30}^{\circ }}=$

1. $\sin {60}^{\circ }$
2. $\cos {60}^{\circ }$
3. $\tan {60}^{\circ }$
4. $\sin {30}^{\circ }$

Q. In Fig., find $\tan P-\cot R$

Q. Given $15\cot A=8$, find $\sin A$ and $\sec A$.

Q. Choose the correct option and justify your choice:
$\frac{1-{\tan }^2{45}^{\circ }}{1+{\tan }^2{45}^{\circ }}=$

1. $\tan {90}^{\circ }$
2. $1$
3. $\sin {45}^{\circ }$
4. $0$

Q. If $\tan A=\frac{7}{8}$, evaluate :
(i) $\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}$ (ii) ${\cot }^2\theta$

Q. Given $\sec \theta =\frac{13}{12}$, calculate all other trignometric ratios.

Q. If $3\cot A=4$, check whether $\frac{1-{\tan }^{2}A}{1+{\tan }^{2}A}={\cos }^{2}A-{\sin }^{2}A$ or not.

Q. If $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=\frac{1}{\sqrt{3}};0^{\circ }<A+B\le {90}^{\circ };A>B$, find $A$ and $B$.

Q. State whether the following are true or false. Justify your answer.
(i) $\sin (A+B)=\sin A+\sin B$
(ii) The value of $\sin \theta$ increases as $\theta$ increases.
(iii) The value of $\cos \theta$ increases as increases.
(iv) $\sin \theta =\cos \theta$ for all values of $\theta$.
(v) $\cot A$ is not defined for $A=0^{\circ }$.

Q. Evaluate:
(i) $\frac{\sin 18^{\circ }}{\cos {72}^{\circ }}$

Q. In $\Delta ABC$, right-angled at $B$, $AB=24$ cm, $BC=7$ cm. Determine:
(i) $\sin A,\cos A$
(ii) $\sin C,\cos C$

Q. Which university did Xuan Zang and I-Qing study at?

Q. Choose the correct option and justify your choice :
$\frac{2\tan {30}^{\circ }}{1-{\tan }^2{30}^{\circ }}=$

1. $\frac{1}{\sqrt{3}}$
2. $\sqrt{3}$
3. $2$
4. $\sqrt{2}$

Q. Show that : (i) $\tan {48}^{\circ }\tan {23}^{\circ }\tan {42}^{\circ }\tan {67}^{\circ }=1$ (ii) $\cos {38}^{\circ }\cos {52}^{\circ }-\sin {38}^{\circ }\sin {52}^{\circ }=0$.