If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is _______.

(a)

\(\frac{1}{\sqrt6}\)

(b)

\(\frac{-1}{\sqrt6}\)

(c)

\(\frac{\sqrt5}{\sqrt6}\)

(d)

\(\frac{-\sqrt5}{\sqrt6}\)

The value of 1 - 2sin²45^o is _______.

(a)

1

(b)

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

(c)

\(\frac14\)

(d)

0

The value 4cos³40^o - 3cos40^o is ________.

(a)

\(\frac{\sqrt3}{2}\)

(b)

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

(c)

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

(d)

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

The value of \(\frac{2\tan30^o}{1+tan^230}\) is _____.

(a)

\(\frac12\)

(b)

\(\frac{1}{\sqrt3}\)

(c)

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

(d)

\(\sqrt3\)

If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is ________.

(a)

1

(b)

0

(c)

\(\frac{\sqrt3}{2}\)

(d)

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

The value of \(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}\) is _______,

(a)

\(\frac{1}{\sqrt3}\)

(b)

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

(c)

\(\frac{\sqrt3}2\)

(d)

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

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is _____.

(a)

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

(b)

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

(c)

\(\frac{4}{5}\)

(d)

\(\frac{5}{4}\)

The value of \(\frac{1}{cosec(-45^o)}\) is _______.

(a)

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

(b)

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

(c)

\(\sqrt2\)

(d)

\(-\sqrt2\)

If p sec 50^o = tan 50^o then p is _______.

(a)

cos 50^o

(b)

sin 50^o

(c)

tan 50^o

(d)

sec 50^o

\(\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}\) is _______.

(a)

cos²x-sin²x

(b)

sin²x-cos²x

(c)

1

(d)

0

Solve : \(\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}\)

Determine the quadrants in which the following degree lie. 1195°

Find the values of each of the following trigonometric ratios. \(\sin { { 300 }^{ o } } \)

Find the values of each of the following trigonometric ratios. \(\sec { \left( { 390 }^{ o } \right) } \)

Find the values of each of the following trigonometric ratios. \(\tan { \left( { -855 }^{ o } \right) } \)

Find the values of each of the following trigonometric ratios.  \(cosec { \left( { 1125 }^{ o } \right) } \)

If \(\sin { A } =\frac { 3 }{ 5 } \) 0 < A < \(\frac{\pi}{2}\)  and \(\cos { B } =\frac { -12 }{ 13 } \) , π < B < \(\frac{3\pi}{2}\) find the values of the following \(\tan(A-B)\)

If \(\sin { A } =\frac { 3 }{ 5 } \) 0\(\frac{\pi}{2}\)  and \(\cos { B } =\frac { -12 }{ 13 } \) , π\(\frac{3\pi}{2}\) find the values of the following sin (A - B)

If \(\cos { A } =\frac { 13 }{ 14 } \)and \(\cos { B } =\frac { 1 }{ 7 } \) where A, B are acute angles, prove that A - B = \(\frac { \pi }{ 3 } \)

Prove that 2 tan 80° = tan 85° - tan 5°

If A + B = 45^° , Prove that (1 + tan A) (1+ tan B) = 2 and hence deduce the value of \(\tan { 22{ \frac { 1 }{ 2 } }^{ ° } } \)

Find all other trigonometrical ratios if \(\sin x=\frac{-2\sqrt6}{5}\) and x lies in III quadrant?

Prove that sin(n+1)x sin(n+2) x+cos(n+1)xcos(n+2)x=cosx.

Prove that cos²2x - cos²6x = sin 4x.sin 8x