Question 11 Mark
What is the maximum value of $\frac{1}{\sec\theta}?$
Answer
View full question & answer→Maximum value of $\frac{1}{\sec\theta}=\cos\theta=1$
Questions
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Question 21 Mark
Write the maximum and minimum values of $\sin\theta.$
Answer
View full question & answer→Maximum and minimum values of $\sin \theta$ lies between -1 and 1.
Question 31 Mark
In Fig. 9.45, $P S=3 cm, Q S=4 cm, \angle P R Q=\theta, \angle P S Q=90^{\circ}, P Q \perp R Q$ and $R Q=9 cm$. Evaluate $\tan \theta$.
Answer
View full question & answer→$\frac{5}{9}$
Question 41 Mark
If $x \sin 60^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}=\frac{\sqrt{3}}{2}$, find the value of $x$.
Answer
View full question & answer→$\frac{2}{\sqrt{3}}$
Question 51 Mark
If $\tan A=\sqrt{3}$, then find the value of $\cos ^2 A-\sin ^2 A$.
Answer
View full question & answer→$-\frac{1}{2}$
Question 61 Mark
Evaluate: $\frac{5 \tan 60^{\circ}}{\left(\sin ^2 60^{\circ}+\cos ^2 60^{\circ}\right) \tan 30^{\circ}}$.
Answer
View full question & answer→15
Question 71 Mark
Evaluate: $\frac{2 \tan 30^{\circ} \sec 60^{\circ} \tan 45^{\circ}}{1-\sin ^2 60^{\circ}}$.
Answer
View full question & answer→$\frac{16}{\sqrt{3}}$
Question 81 Mark
If $\sin (A-B)=\frac{1}{2}, \cos (A+B)=\frac{1}{2} ; \quad 0 < A+B \leq 90^{\circ} . A > B ;$ find $\angle A$ and $\angle B$.
Answer
View full question & answer→$\angle A=45^{\circ}, \angle B=15^{\circ}$
Question 91 Mark
Evaluate: $\frac{5 \cos ^2 60^{\circ}+4 \sec ^2 30^{\circ}-\tan ^2 45^{\circ}}{\sin ^2 30^{\circ}+\sin ^2 60^{\circ}}$
Answer
View full question & answer→$\frac{67}{12}$
Question 101 Mark
If $A=60^{\circ}$ and $B=30^{\circ}$, verify that $\sin (A+B)=\sin A \cos B+\cos A \sin B$.
View full question & answer→Question 111 Mark
Evaluate: $2 \sqrt{2} \cos 45^{\circ} \sin 30^{\circ}+2 \sqrt{3} \cos 30^{\circ}$
Answer
View full question & answer→4
Question 121 Mark
If $2 \sin (A+B)=\sqrt{3}$ and $\cos (A-B)=1$, then find the measures of angles $A$ and $B$. $0 \leq A, B,(A+B) \leq 90^{\circ}$.
Answer
View full question & answer→$A=B=\frac{\pi}{6}$
Question 131 Mark
Evaluate: $2 \sin ^2 30^{\circ} \sec 60^{\circ}+\tan ^2 60^{\circ}$
Answer
View full question & answer→4
Question 141 Mark
If $\sin A=\frac{3}{4}$, calculate $\sec A$.
Answer
View full question & answer→$\frac{4}{\sqrt{7}}$
Question 151 Mark
Evaluate: $\sin ^2 60^{\circ}+2 \tan 45^{\circ}-\cos ^2 30^{\circ}$.
Answer
View full question & answer→2
Question 161 Mark
If $\tan A=\frac{5}{12}$, find the value of $(\sin A+\cos A) \sec A$.
Answer
View full question & answer→$\frac{17}{12}$
Question 171 Mark
Write the value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots . . . \cos 179^{\circ} \cos 180^{\circ}$.
Answer
View full question & answer→0
Question 181 Mark
Write the acute angle $\theta$ satisfying $\sqrt{3} \sin \theta=\cos \theta$.
Answer
View full question & answer→$30^{\circ}$
Question 191 Mark
If $\cot \theta=\frac{1}{\sqrt{3}}$, write the value of $\frac{1-\cos ^2 \theta}{2-\sin ^2 \theta}$.
Answer
View full question & answer→$\frac{3}{5}$
Question 201 Mark
Given $\tan \theta=\frac{1}{\sqrt{5}}$, what is the value of $\frac{\operatorname{cosec}^2 \theta-\sec ^2 \theta}{\operatorname{cosec}^2 \theta+\sec ^2 \theta}?$
Answer
View full question & answer→$\frac{2}{3}$
Question 211 Mark
If $3 \cot \theta=4$, find the value of $\frac{4 \cos \theta-\sin \theta}{2 \cos \theta+\sin \theta}$.
Answer
View full question & answer→$\frac{13}{11}$
Question 221 Mark
If $\cos \theta=\frac{2}{3}$, find the value of $\frac{\sec \theta-1}{\sec \theta+1}$.
Answer
View full question & answer→$\frac{1}{5}$
Question 231 Mark
If $\tan \theta=\frac{4}{5}$, find the value of $\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}$.
Answer
View full question & answer→$\frac{1}{9}$
Question 241 Mark
What is the maximum value of $\frac{1}{\operatorname{cosec} \theta}$?
Answer
View full question & answer→1
Question 251 Mark
What is the maximum value of $\frac{1}{\sec \theta}$?
Answer
View full question & answer→1
Question 261 Mark
Write the maximum and minimum values of $\cos \theta$
Answer
View full question & answer→-1 and 1
Question 271 Mark
Write the maximum and minimum values of $\sin \theta$
Answer
View full question & answer→-1 and 1