Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Q. If $\tan A=\frac{x\sin B}{1-x\cos B}$ and $\tan B=\frac{y\sin A}{1-y\cos A}$ then $\frac{\sin A}{\sin B}=$

1. 
2. 
3. 
4. 

Q. If ${180}^{\circ }$ < $\theta$ < ${270}^{\circ }$ and $\sin \theta =-\frac{5}{13}$ then 5 ${\cot }^2\theta +12\tan \theta +13cosec\theta$ =

1. 0
2. -1
3. 1
4. 2

Q.

If $sinx+cosecx=2$, then $si{n}^{n}x+cose{c}^{n}x$ is equal to

1. 1

2. 

3. 

4. 2

Q. The expression $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$ can be written as :

1. $\sin A\cdot \cos A+1$
2. $\sec A\cdot \text{cosec}A+1$
3. $\tan A+\cot A$
4. $\sec A+\text{cosec}A$

Q. The numerical value of $(1-\cos x)(1+\cos x)(1+{\cot }^{2}x)$ is

1. $0$
2. $1$
3. $2$
4. $3$

Q. The angle (in degree) between the hour hand and the minute hand in a circular clock at $03:25$ hours is

1. ${67.5}^{\circ }$
2. ${75}^{\circ }$
3. ${47.5}^{\circ }$
4. ${52.5}^{\circ }$

Q. The expression $\sin A(1+\tan A)+\cos A(1+\cot A)$ is equivalent to

1. $\sin A+\cos A$
2. $\sec A+\tan A$
3. $\text{cosec}A+\cot A$
4. $\text{cosec}A+\sec A$

Q. The numerical value of $(1+\cot x-\text{cosec}x)(1+\tan x+\sec x)$ is

Q. The value of $\sin \frac{\pi }{5}\sin \frac{2\pi }{5}\sin \frac{3\pi }{5}\sin \frac{4\pi }{5}$ is

1. $\frac{5}{16}$
2. $\frac{3}{16}$
3. $\frac{11}{16}$
4. $\frac{13}{16}$

Q. If $\frac{1+\sin 2x}{1-\sin 2x}={\cot }^2(a+x)$$\forall x\in R-(n\pi +\frac{\pi }{4}),$ $n\in N$ then the possible value of $a$ is

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