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

Q.

Determine the quadrant when the terminal side of the angle lies according to the following conditions: $\tan \left(t\right)>0,cosec\left(t\right)<0$

1. Quadrant $I$

2. Quadrant $III$

3. Quadrant $IV$

4. Quadrant $II$

Q.

$ta{n}^2\theta +co{t}^2\theta$ is

1. None of these

2. 

3. 

4. 

Q.

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

1. 2

2. 

3. 

4. 1

Q. The value of $\frac{\cos {15}^{\circ }+\sin {15}^{\circ }}{\cos {15}^{\circ }-\sin {15}^{\circ }}$ is

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

Q. The value of $(\cos {75}^{\circ }-\cos {15}^{\circ }{)}^2+(\sin {75}^{\circ }-\sin {15}^{\circ }{)}^2$ is

1. $0$
2. $1$
3. $\frac{1}{2}$
4. $-1$

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

Q. The value of $\cos (n+1)\alpha \cos (n-1)\alpha +\sin (n+1)\alpha \sin (n-1)\alpha$ is

1. $\cos 2n\alpha$
2. $\sin 2n\alpha$
3. $\cos 2\alpha$
4. $\sin 2\alpha$

Q. The value of ${\sin }^{2}A+{\sin }^2(A+B)-2\sin A\cos B\sin (A+B)$ when $B={45}^{\circ }$ is

1. $\frac{1}{\sqrt{2}}$
2. $\frac{1}{2}$
3. ${\sin }^{2}A+\frac{1}{\sqrt{2}}$
4. ${\sin }^{2}A+\frac{1}{2}$