Trigonometric identities

Q. If $cosec\theta -cot\theta =\frac{1}{2},0<\theta <\frac{\pi }{2}$, then $cos\theta$ is equal to

1. $\frac{3}{5}$
2. $-\frac{3}{5}$
3. $-\frac{5}{3}$
4. $\frac{5}{3}$

Q.

Statement1 : $co{s}^{2}A$ + $si{n}^{2}A$ = 1

Statement2 : $se{c}^{2}A$ + $ta{n}^{2}A$ = 1

1. Statement1 is true and Statement2 is false

2. Statement2 is true and Statement1 is false

3. Both Statement1 are Statement2 are true

4. Both Statement1 are Statement2 are false

Q. Prove that $\frac{1+sec\theta -tan\theta }{1+sec\theta +tan\theta }=\frac{1-sin\theta }{cos\theta }$

Q.

Solve for $\theta$ if $4co{s}^2\theta$ + 2$sin\theta$ – 4 = 0, where 0 $\le$ $\theta$ $\le$ 90.

1. $0^{\circ }$

2. ${30}^{\circ }$

3. both (a) and (b)

4. cannot be determined

Q.

Evaluate 1 – 2$sin\theta$ $cos\theta$ if $sin\theta$ = $cos\theta$.

1. - 1

2. 0

3. 2

4. 1

Q.

Statement1: $cose{c}^{2}A$ - $co{t}^{2}A$ = 1

Statement2: 1 + $ta{n}^{2}A$ = $se{c}^{2}A$

1. Both statements are false.

2. Statement 1 is true and Statement 2 is false.

3. Both statements are true.

4. Statement 1 is false and Statement 2 is true.

Q.

If $sin\theta +si{n}^2\theta =1$, then $co{s}^4\theta +co{s}^2\theta -1=$

___

1. 2

2. 1

3. 0

4. -1

Q. $\frac{si{n}^2{63}^{\circ }+si{n}^2{27}^{\circ }}{co{s}^2{17}^{\circ }+co{s}^2{73}^{\circ }}$ =

1. \N
2. 1
3. $\frac{1}{2}$