\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

(a)

\(\sqrt{2}\)

(b)

\(\sqrt{3}\)

(c)

2

(d)

4

The maximum value of 4sin²x + 3 cos²x + \(sin\frac { x }{ 2 } +cos\frac { x }{ 2 } \) is

(a)

\(4 + \sqrt{2}\)

(b)

\(3+ \sqrt{2}\)

(c)

9

(d)

4

cos1⁰ + cos2⁰ + cos3⁰ +: : : + cos179⁰ =

(a)

0

(b)

1

(c)

-1

(d)

89

cos 2ፀ cos 2ф + sin²(ፀ - ф) - sin²(ፀ + ф) is equal to

(a)

sin2(ፀ+\(\phi \))

(b)

cos2(ፀ+\(\phi \))

(c)

sin2(ፀ-\(\phi \))

(d)

cos2(ፀ-\(\phi \))

If tan α and tan β are the roots of x² + ax + b = 0; then \(\frac { sin(\alpha +\beta ) }{ sin\alpha sin\beta } \) is equal to

(a)

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

(b)

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

(c)

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

(d)

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

If f(ፀ) = |sin ፀ| + |cos ፀ|, ፀ\(\in \)R, then f(ፀ) is in the interval     

(a)

[0, 2]

(b)

[1,\(\sqrt { 2 } \)]

(c)

[1, 2]

(d)

[0, 1]

A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

(a)

10\(\pi \) seconds

(b)

20\(\pi \) seconds

(c)

5\(\pi \) seconds

(d)

15\(\pi \) seconds

In a ΔABC, if
(i) \(sin\frac { A }{ 2 } sin\frac { B }{ 2 } sin\frac { C }{ 2 } \) > 0
(ii) sin A sin B sin C > 0, Then 

(a)

Both (i) and (ii) are true

(b)

Only (i) is true

(c)

Only (ii) is true

(d)

Neither (i) nor (ii) is true

If tan x = \(\frac { -1 }{ \sqrt { 5 } } \) and x lies in the IV quadrant, then the value of cos x is ___________

(a)

\(\sqrt { \frac { 5 }{ 6 } } \)

(b)

\(\frac { 2 }{ \sqrt { 6 } } \)

(c)

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

(d)

\(\frac { 1 }{ \sqrt { 6 } } \)

If cosec x + cot x = \(\frac { 11 }{ 2 } \) then tan x = ___________

(a)

\(\frac { 21 }{ 22 } \)

(b)

\(\frac { 15 }{ 16 } \)

(c)

\(\frac { 44 }{ 117 } \)

(d)

\(\frac { 117 }{ 44 } \)

2tan^-1\(\left( \frac { 1 }{ 5 } \right) \) is equal to _______________

(a)

tan\(\left( \frac { 5 }{ 12 } \right) \)

(b)

\(\frac { 5 }{ 12 } \)

(c)

\(\tan^{-1}\left({5 \over 12}\right)\)

(d)

tan^-1\(\frac { 2 }{ 5 } \)

If sin(45 ° + 10°) - sin(45° -10°) = \(\sqrt{2}\)sin x then x is ___________ 

(a)

0^o

(b)

5°

(c)

10°

(d)

15°

If 2 sin θ + 1 = 0 and \(\sqrt{3}\) tan θ = 1, then the most general value of θ is _______________

(a)

\(n\pi\pm\frac{\pi}{6}\)

(b)

\(n\pi+(-1)^n\frac{7\pi}{6}\)

(c)

\(2n\pi+\frac{7\pi}{6}\)

(d)

\(2n\pi+\frac{11\pi}{6}\)

If (A + B) = \(\frac{\pi}{4}\), (cot A - 1) (cot B - 1) = _______________

(a)

0

(b)

-2

(c)

2

(d)

1

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is _______________

(a)

0

(b)

1

(c)

2

(d)

3