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

(a)

0

(b)

1

(c)

-1

(d)

89

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 = \(\frac { 1 }{ 4 } \)

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)

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

In a triangle ABC, sin²A + sin²B + sin²C = 2, then the triangle is

(a)

equilateral triangle

(b)

isosceles triangle

(c)

right triangle

(d)

scalene triangle

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

If A + B = 45° then tan A - tan B + tan A tan B is _______________

(a)

2

(b)

0

(c)

1

(d)

-1

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)

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

In a \(\triangle\) ABC, C = 90° then the value of sin A + sin B - 2\(\sqrt{2} cos{A\over2}cos {B\over 2}is\) _______________

(a)

-1

(b)

1

(c)

0

(d)

\({1\over 2}\)

The general solution of cosec_\(\theta\) = -2 is _______________

(a)

\(2n\pi +(-1)^n({\pi\over 6})\)

(b)

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

(c)

\(2n\pi \pm({\pi\over 6})\)

(d)

\(-{\pi\over 6}+n\pi\)

Find the values of cos x and tan x if \(\sin x=-\frac{3}{5}\) and \(\pi < x < \frac{3\pi}{2}\)

Evaluate tan 480⁰

cot B - cot A = b, tan A - tan B = a, find cot (A - B).

Simplify: cos A + cos (120° + A) + cos (120° - A)

Find the values of sin(480°).

Find the values of sin(-1110°).

If any \(\triangle ABC\) prove that \(\frac { \sin { B } }{ \sin { C } } =\frac { c-a\cos { B } }{ b-a\cos { C } } \).

Two slopes leave a port at the same time one goes 24 km/hr in the direction N 45^o E and other travels 32 km/hr in the direction S 75^o E. Find the distance between the ships at the end of 3 hours.

Solve: sin 2x + cos x = 0

Prove that cos^-1 x = \(2\sin ^{ -1 }{ \sqrt { \frac { 1-x }{ 2 } } } =2\cos ^{ -1 }{ \sqrt { \frac { 1+x }{ 2 } } } \)

Prove that \(\tan ^{ -1 }{ \left( \frac { x }{ \sqrt { { { a }^{ 2 }-{ x }^{ 2 } } } } \right) } =\sin ^{ -1 }{ \left( \frac { x }{ a } \right) } \)

Prove that \(cos\left( \frac { \pi }{ 4 } -A \right) cos\left( \frac { \pi }{ 4 } -B \right) -sin\left( \frac { \pi }{ 4 } -A \right) sin\left( \frac { \pi }{ 4 } -B \right) \)

If 3 tan A tan B = 1, prove that 2 cos(A+B) = cos(A-B) 

Prove that \(\cos x\cos \left( \frac { \pi }{ 3 } -x \right) cos\left( \frac { \pi }{ 3 } +x \right)=\frac14 cos3x\)