Trigonometric Ratios of Compound Angles

Q. In $\Delta$ ABC, if cot A + cot B + cot C = $\sqrt{3}$, then ABC is an

1. Right angled triangle
2. Eequilateral triangle
3. Isosceles
4. None

Q.

If $\alpha ,\beta \gamma ,ϵ(0,\frac{\pi }{2}),then\frac{sin(\alpha +\beta +\gamma )}{sin\alpha +sin\beta +sin\gamma }is$

1. < 1

2. None of these

3. > 1

4. = 1

Q. If $sin\alpha =\frac{1}{\sqrt{5}}andsin\beta =\frac{3}{5},then\beta -\alpha$ lies in the interval

1. 
   
2. 
3. 
   
4. 

Q. $\sqrt{3}cosec{20}^{\circ }-sec{20}^{\circ }=$

1. 
2. 
3. 
4. 

Q. ${\sin }^2\alpha +{\cos }^2(\alpha +\beta )+2\sin \alpha .\sin \beta \cos (\alpha +\beta )=$

1. 
2. 
3. 
4. 

Q. ${\cos }^2{1}^{\circ }+{\cos }^2{2}^{\circ }+{\cos }^2{3}^{\circ }+....+{\cos }^2{90}^{\circ }=$

1. 0
2. 1
3. 45
4. 

Q. If $\frac{x}{cos\theta }=\frac{y}{cos(\theta -\frac{2\pi }{3})}=\frac{z}{cos(\theta +\frac{2\pi }{3})},$ then x + y + z=

1. None of these
2. 1
3. 0
4. -1

Q. If $tan\theta =\frac{sin\alpha -cos\alpha }{sin\alpha +cos\alpha }thensin\alpha +cos\alpha andsin\alpha -cos\alpha$
and must be equal to

1. 
2. 
3. 
4. 

Q. $(1+cos\frac{\pi }{8})(1+cos\frac{3\pi }{8})(1+cos\frac{5\pi }{8})(1+cos\frac{7\pi }{8})$=

1. 
2. 
3. 
4. 

Q. If A + B = ${225}^{\circ }$, then $\frac{\cot A}{1+\cot A}.\frac{\cot B}{1+\cot B}=$

1. 0
2. 
3. 
4.