Untitled

 2 mark

| -0.25 mark |

 60 minutes

Question 1:

Given \(15\cot A = 8\), find \(\sin A\) and \(\sec A\).

Question 2:

Given \( \sec \theta=\frac{13}{12} \), calculate all other trigonometric ratios.

Question 3:

What is the known/given? \(\cot \theta = \frac{7}{8}\)

What is the unknown? Value of
(i) \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\), and
(ii) \(\cot^{2} \theta\).

Question 4:

In \( \triangle \mathrm{ABC} \), right-angled at \( \mathrm{B}, \mathrm{AB}=24 \mathrm{~cm}, \mathrm{BC}=7 \mathrm{~cm} \), determine:
(i) \( \sin \mathrm{A}, \cos \mathrm{A} \)
(ii) \( \sin C, \cos C \)

Question 5:

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

Question 6:

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

Question 7:

In the 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) \( \cos A \cos C - \sin A \sin C \)

Question 8:

(v) \( \frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sec ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}} \)

Question 9:

(iv) \( \frac{\sin 30^{\circ}+\tan 45^{\circ}-\operatorname{cosec} 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}-\cot 45^{\circ}} \)

Question 10:

(iii) \( \frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}} \)

Question 11:

\( 2 \tan^{2}45^{\circ} + \cos^{2}30^{\circ} - \sin^{2}60^{\circ} \)

Question 12:

\( \frac{1-\tan^{2}45^{\circ}}{1+\tan^{2}45^{\circ}} \)

Question 13:

\( \sin 2A = 2 \sin A \) is true when A =

Question 14:

\( \frac{2 \tan 30^{\circ}}{1+\tan^{2}30^{\circ}} \)

Question 15:

\( \frac{2 \tan 30^{\circ}}{1-\tan^{2} 30^{\circ}} \)

Question 16:

\( \cos 48^{\circ}-\sin 42^{\circ} \)

Question 17:

(i) \( \frac{\sin 18^{\circ}}{\cos 72^{\circ}} \)

Question 18:

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

Question 19:

(ii) \( \frac{\tan 26^{\circ}}{\cot 64^{\circ}} \)

Question 20:

\( \operatorname{cosec} 31^{\circ}-\sec 59^{\circ} \)

Question 21:

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

Question 22:

(i) \( \tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} \)

Question 23:

(ii) \( \cos 38^{\circ} \cos 52^{\circ}-\sin 38^{\circ} \sin 52^{\circ} \)

Question 24:

If \( \sec 4A = \csc(A - 20^\circ) \), where 4A is an acute angle, find the value of A.

Question 25:

If \( \tan A = \cot B \), prove that \( A + B = 90^{\circ} \).

Question 26:

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