If $\theta$ is an acute angle and $7+4\sin\theta=9$, then the value of $\theta$ is:
[1]
The value of $\tan^{2}\theta-(\frac{1}{\cos\theta}\times\sec\theta)$ is:
[1]
(a) If $x\cos 60^{\circ}+y\cos 0^{\circ}+\sin 30^{\circ}-\cot 45^{\circ}=5$, then find the value of $x+2y$.
OR
(b) Evaluate: $\frac{\tan^{2}60^{\circ}}{\sin^{2}60^{\circ}+\cos^{2}30^{\circ}}$
[2]
(a) Prove that: $\frac{\tan\theta}{1-\cot\theta}+\frac{\cot\theta}{1-\tan\theta}=1+\sec\theta\csc\theta$
OR
(b) Prove that: $\frac{\sin A+\cos A}{\sin A-\cos A}+\frac{\sin A-\cos A}{\sin A+\cos A}=\frac{2}{2\sin^{2}A-1}$
[3]
If $\sec~\theta-\tan~\theta=m$, then the value of $\sec~\theta+\tan~\theta$ is:
[1 mark]
If $\cos(\alpha+\beta)=0$, then value of $\cos(\frac{\alpha+\beta}{2})$ is equal to :
[1 mark]
Evaluate: $2\sqrt{2}\cos~45^{\circ}\sin~30^{\circ}+2\sqrt{3}\cos~30^{\circ}$
[2 marks]
If $A=60^{\circ}$ and $B=30^{\circ}$, verify that :
$\sin(A+B)=\sin~A~\cos~B+\cos~A~\sin~B$
[2 marks]
Prove that: $\frac{\tan~\theta}{1-\cot~\theta}+\frac{\cot~\theta}{1-\tan~\theta}=1+\sec~\theta~\csc~\theta$
[3 marks]
If \( 2 \tan A=3 \), then the value of \( \frac{4 \sin A+3 \cos A}{4 \sin A-3 \cos A} \) is
[1 mark]
\( \left[\frac{3}{4}\tan^{2}30^{\circ}-\sec^{2}45^{\circ}+\sin^{2}60^{\circ}\right] \) is equal to
[1 mark]
(a) If \( \sin \theta+\cos \theta=\sqrt{3} \), then find the value of \( \sin \theta \cdot \cos \theta \).
OR
(b) If \( \sin \alpha=\frac{1}{\sqrt{2}} \) and \( \cot \beta=\sqrt{3} \), then find the value of \( \operatorname{cosec} \alpha+\operatorname{cosec} \beta \).
[2 marks]
Prove that: \( \frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}=\frac{1+\sin \theta}{\cos \theta} \)
[3 marks]