The radian measure of 37^o30^' is ______.

The value of \(\sin(-420^o)\) is _______.

The value of cos²45^o - sin²45^o is_______.

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

If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is  _____.

Prove that \(\tan^{-1}\left(\frac{4}{3}\right)-\tan^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}\)

Convert the following degree measure into radian measure 150^o

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

Prove that \(sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.\)

Evaluate : \(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

Prove that  \(2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 } \)

Prove that: \(\cos { { 510 }^{ o } } \cos { { 330 }^{ o } } +\sin { { 390 }^{ o } } \cos { { 120 }^{ o } } =-1\)

Show that \(\tan\left(\frac{\pi}{3}+x\right)\tan\left(\frac{\pi}{3}-x\right)=\frac{2\cos2x+1}{2\cos2x-1}\)

Prove that \(\frac{\sin5x+\sin3x}{\cos5x+\cos3x}=\tan4x\)

If tan(x + y) = 42 and x = tan^–1(2), then find y

If \(\cos(\alpha+\beta)=\frac45\) and \(\sin(\alpha-\beta)=\frac{5}{13}\) where \((\alpha+\beta)\) and \((\alpha-\beta)\) are acute, then find \(\tan2\alpha\)

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)

Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1.

Prove that cos 4x = 1 - 8 sin²x cos²x.