The degree measure of \(\frac{\pi}{8}\) is ______.

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

The value of sin 15^o cos 15^o is ______.

The value of sec A sin(270^o + A) is ______.

If sin A + cos A = 1, then sin 2A is equal to _______.

Find the principal value of the following \(\sin ^{-1}\left(-\frac{1}{2}\right)\)

Find the principal value of the following cosec^-1(2)

Determine the quadrants in which the following degree lie. -140°

Find the value of \(\cos\left(\frac{5\pi}{12}\right)\)

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

Prove that \(\sqrt3\) cosec 20^o- sec 20^o = 4

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

Prove that:  \(\sin { \theta } \cos { \theta } \left\{ \sin { \left( \frac { \pi }{ 2 } -\theta \right) } \csc { \theta } +\cos { \left( \frac { \pi }{ 2 } -\theta \right) \sec { \theta } } \right\} =1\)

If \(\alpha\) and \(\beta\) are acute angles such that \(\tan\alpha=\frac{m}{m+1}\) and \(\tan\beta=\frac{1}{2m+1}\), prove that \(\alpha+\beta=\frac{\pi}{4}\)

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  \(\frac { \sin { \left( { 180 }^{ o }+A \right) \cos { \left( { 90 }^{ o }-A \right) \tan { \left( { 270 }^{ o }-A \right) } } } \quad \quad }{ \sec { \left( { 540 }^{ o }-A \right) \cos { \left( { 360 }^{ o }+A \right) \ cosec { \left( { 270 }^{ o }+A \right) } } } } =-\sin { A } \cos ^{ 2 }{ A } \)

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 cos²2x - cos²6x = sin 4x.sin 8x

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