If tan40⁰ = λ, then \(\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } } \) =

(a)

\(\frac { 1-\lambda ^{ 2 } }{ \lambda } \)

(b)

\(\frac { 1+{ \lambda }^{ 2 } }{ \lambda } \)

(c)

\(\frac { 1+{ \lambda }^{ 2 } }{ 2\lambda } \)

(d)

\(\frac { 1-{ \lambda }^{ 2 } }{ 2\lambda } \)

Let f_k(x) = \(\frac { 1 }{ k } \)[sin^kx + cos^kx] where x\(\in \)R and k ≥ 1. Then f₄(x) - f₆(x) =

(a)

\(\frac { 1 }{ 4 } \)

(b)

\(\frac { 1 }{ 12 } \)

(c)

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

(d)

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

Which of the following is not true?

(a)

​​​​​​sinፀ = \(-\frac { 3 }{ 4 } \)

(b)

cosፀ = -1

(c)

tanፀ = 25

(d)

secፀ = \(\frac { 1 }{ 4 } \)

\(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) is equal to

(a)

cos 2x

(b)

cos x

(c)

cos 3x

(d)

2 cos x

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

The value of sin²\(\frac { 5\pi }{ 12 } -sin^{ 2 }\frac { \pi }{ 12 } \) is ___________

(a)

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

(b)

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

(c)

1

(d)

0

\(\frac { cos3x }{ 2cos2x-1 } \) is _______________

(a)

cos x

(b)

sin x

(c)

tan x

(d)

cot x

The value of sin\({\pi\over 48}cos {\pi \over 48} cos {\pi \over 24}cos {\pi \over 12}cos{\pi \over 6}cos {\pi \over 3}\) is _____________ 

(a)

\(\sqrt{3}\over32\)

(b)

\(\sqrt{3}\over64\)

(c)

_{\({3}\over32\)}

(d)

_{\({3}\over64\)}

If sin θ = sin \(\alpha\), then the angles θ and \(\alpha\) are related by _______________

(a)

\(\theta=n\pi\pm\alpha\)

(b)

\(\theta=2n\pi+(-1)^n\alpha\)

(c)

\(\alpha=n\pi\pm(-1)^n\theta\)

(d)

\(\theta=(2n+1)\pi+\alpha\)

If in a triangle a = 5, b = 4 and cos(A - B) = \(\frac{31}{32}\) then the third side C is equal to _______________

(a)

5

(b)

6

(c)

3

(d)

12

Identify the quadrant in which an angle of each given measure lies; 328⁰

A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30⁰. If after 100 km, the target has an angle of depression of 60⁰, how far is the target from the fighter jet at that instant?

If \(\sin { x } =\frac { 15 }{ 17 } \) and \(\cos {y } =\frac { 12 }{ 13 } \), 0 < x < \(\frac{\pi}{2}\), 0 < y < \(\frac{\pi}{2}\), find the value of tan (x + y)

For each given Angle, find a coterminal angle with a measure of \(\theta\) such that \(0^o\le \theta \le 360°\) 
395⁰ 

If sin \(\theta\) + cos \(\theta\) = m, show that cos⁶\(\theta\) + sin⁶\(\theta\)  = \(\frac { 4-3({ m }^{ 2 }-1)^{ 2 } }{ 4 } \), where m² \(\le \) 2

If x = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n } } \theta ;\) y = \(y=\sum _{ n=0 }^{ \infty }{ { sin }^{ 2n } } \theta \)  and z = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n }\theta } \) sin²ⁿ\(\theta \), 0 < \(\theta \) < \(\frac { \pi }{ 2 } \), then show that xyz = x+y+z  
Hint :1+x+x²+x³+.......= \(\frac { 1 }{ 1-x } \), where \(\left| x\right| \)< 1].

If sec \(\theta\) + tan \(\theta\) = p, obtain the values of sec \(\theta\), tan \(\theta\) and sin \(\theta\) in terms of p

Find the value of tan\(\frac { \pi }{ 2 } \).

In a ΔABC if a = 3, b = 5 and c = 7, find cos A and cos B.

Evaluate sin\(\left( cos^{ -1 }\left( \frac { 3 }{ 5 } \right) \right) \)