tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

(a)

sec\(\theta \)

(b)

\(cot^{ 2 }\theta \)

(c)

sin\( \theta \)

(d)

\(cot\theta \)

If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

(a)

25

(b)

\(\frac { 1 }{ 25 } \)

(c)

5

(d)

1

If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

(a)

\(\frac { -3 }{ 2 } \)

(b)

\(\frac { 3 }{ 2 } \)

(c)

\(\frac { 2 }{ 3 } \)

(d)

\(\frac { -2 }{ 3 } \)

a cot \(\theta \) + b cosec\(\theta \) = p and b cot \(\theta \) + a cosec\(\theta \) = q then p²- q² is equal to 

(a)

a² - b²

(b)

b² - a²

(c)

a² + b²

(d)

b - a

The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

(a)

\(\sqrt { 3 } \) b

(b)

\(\frac { b }{ 3 } \)

(c)

\(\frac { b }{ 2 } \)

(d)

\(\frac { b }{ \sqrt { 3 } } \)

A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

(a)

41.92 m

(b)

43.92 m

(c)

43 m

(d)

45.6 m

The angle of elevation of a cloud from a point h metres above a lake is \(\beta \). The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

(a)

\(\frac { h\left( 1+tan\beta \right) }{ 1-tan\beta } \)

(b)

\(\frac { h\left( 1-tan\beta \right) }{ 1+tan\beta } \)

(c)

h tan(45°-\(\beta \))

(d)

none of these 

If sin A = \(\frac{1}{2}\), then the value of cot A is ___________

(a)

\(\sqrt{3}\)

(b)

\(\frac{1}{\sqrt{3}}\)

(c)

\(\frac{\sqrt{3}}{2}\)

(d)

1

Given that sinθ = \(\frac{a}{b}\), then cosθ is equal to ___________

(a)

\(\frac { b }{ \sqrt { { b }^{ 2 }-{ a }^{ 2 } } } \)

(b)

\(\frac { b }{ a } \)

(c)

\(\frac { \sqrt { { b }^{ 2 }-{ a }^{ 2 } } }{ b } \)

(d)

\(\frac { b }{ \sqrt { { b }^{ 2 }-{ a }^{ 2 } } } \)

If cos9∝ = sin∝ and 9∝ < 90^o, then the value of tan t∝ is

(a)

\(\frac{1}{\sqrt{3}}\)

(b)

\({\sqrt{3}}\)

(c)

1

(d)

0

Given that sin ∝ = \(\frac{1}{2}\) and cos β = \(\frac{1}{2}\), then the value of (∝ + β) is ___________

(a)

0^o

(b)

30^o

(c)

60^o

(d)

90^o

If 4 tan θ = 3, then \(\left( \frac { 4sin\theta -cos\theta }{ 4sin\theta +cos\theta } \right) \) is equal to ___________

(a)

\(\frac{2}{3}\)

(b)

\(\frac{1}{3}\)

(c)

\(\frac{1}{2}\)

(d)

\(\frac{3}{4}\)

Sin(45^o+ θ ) - cos(45^o - θ) is equal to ___________

(a)

2cos θ

(b)

0

(c)

2sin θ

(d)

1

The maximum value of sin θ is ___________

(a)

\(\frac{1}{2}\)

(b)

\(\frac{\sqrt{3}}{2}\)

(c)

1

(d)

\(\frac{1}{\sqrt2}\)

The value of sin² θ + \(\frac { 1 }{ 1+{ tan }^{ 2 }\theta } \) of ___________

(a)

sin²θ

(b)

cos²θ

(c)

secθ

(d)

1