Basic Trigonometric Identities

Q. If $\sin \theta +{\sin }^2\theta =1,$ then ${\cos }^2\theta +{\cos }^4\theta =$

1. 1
2. 0
3. 
4. 2

Q.

If $\frac{3\pi }{4}<\alpha <\pi$, then $\sqrt{cose{c}^2\alpha +2cot\alpha }$ is equal to

1. 

2. 

3. 

4. 

Q. If $\sec \theta =a+\frac{1}{4a}then\sec \theta +\tan \theta =$

1. a
2. 3a
3. 4a
4. 2a

Q.

If $co{s}^6\alpha +si{n}^6\alpha +Ksi{n}^{2}2\alpha =1$, then K=

1. 

2. 

3. 

4. 2

Q. If $\sin \theta ,\cos \theta$ are the roots of the equation $a{x}^2-bx+c=0,$ then the relation among a, b, c is

1. 
2. 
3. 
4. 

Q. If $\sin x+{\sin }^{2}x=1$, then the value of expression ${\cos }^{12}x+3{\cos }^{10}x+3{\cos }^{8}x+{\cos }^{6}x-1$ is equal to

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

Q.

$Ifaco{s}^3\alpha +3acos\alpha si{n}^2\alpha =mandasi{n}^3\alpha +3aco{s}^2\alpha sin\alpha =n,then(m+n{)}^{\frac{2}{3}}+(m-n{)}^{\frac{2}{3}}isequalto$

1. 

2. 

3. 

4. 

Q.

Find the value of $se{c}^{2}x$ - $cose{c}^{2}x$.

1. +

2. -

3. -

4. 1

Q. If $tan\theta =\sqrt{\frac{3}{2}}$, the sum of the infinite series 1 + 2 $(1-cos\theta )+3(1-cos\theta {)}^2+4(1-cos\theta {)}^3+....\infty$ is

1. 
2. 
3. 
4. 

Q.

If $(\sin x+\cos x=a)$, then $1+2\sin x\cos x=a^2$

1. False

2. True