The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

(a)

 \(ta{ n }^{ 2 }\theta \)

(b)

1

(c)

\(cot^{ 2 }\theta \)

(d)

0

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

(a)

2a

(b)

3a

(c)

0

(d)

2ab

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)

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

(1 + tan \(\theta \) + sec\(\theta \)) (1 + cot\(\theta \) - cosec\(\theta \)) is equal to 

(a)

0

(b)

1

(c)

2

(d)

-1

If the ratio of the height of a tower and the length of its shadow is \(\sqrt{3}: 1\), then the angle of elevation of the sun has measure

(a)

45°

(b)

30°

(c)

90°

(d)

60°

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

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

(a)

\(\sqrt { 2 } \) x

(b)

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

(c)

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

(d)

2x

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

(a)

9

(b)

7

(c)

5

(d)

3

If cos A = \(\frac{4}{5}\), then the value of tan A is ___________

(a)

\(\frac{3}{5}\)

(b)

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

(c)

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

(d)

\(\frac{5}{3}\)

The value of the expression [cosec (75^o + θ) - sec (15^o - θ) - tan (55^o + θ) + cot(35^o - θ] is ___________

(a)

-1

(b)

0

(c)

1

(d)

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

If cos (∝ - β) =, then sin (∝ - β)  can be reduced to ___________

(a)

cos β

(b)

cos 2β

(c)

sin ∝

(d)

sin 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

If sin A + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is ___________

(a)

1

(b)

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

(c)

2

(d)

3

The value of the expression \(\left[ \frac { { sin }^{ 2 }{ 22 }^{ o }+{ sin }^{ 2 }{ 68 }^{ o } }{ { cos }^{ 2 }{ 22 }^{ 0 }+{ cos }^{ 2 }{ 68 }^{ 0 } } +{ sin }^{ 2 }{ 63 }^{ o+ }{ cos }63^{ 0 }{ sin27 }^{ 0 } \right] \)is ___________

(a)

3

(b)

2

(c)

1

(d)

0

If cotθ = b/a then value of \(\frac { cos\theta +sin\theta }{ cos\theta -sin\theta } \) a

(a)

\(\frac{b-c}{b+a}\)

(b)

b-a

(c)

b+a

(d)

-\(\frac{b+c}{b-a}\)