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

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

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

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

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

Convert the following degree measure into radian measure 60^o

Evaluate : \(\cos\left[\tan^{-1}\left(\frac34\right)\right]\)

Find the values of the following  cot 75°

Prove that  \(\sec { \left( \frac { 3\pi }{ 2 } -\theta \right) } \sec { \left( \theta -\frac { 5\pi }{ 2 } \right) } +\tan { \left( \frac { 5\pi }{ 2 } +\theta \right) } \tan { \left( \theta -\frac { 5\pi }{ 2 } \right) } =-1\)

Express each of the following as the sum or difference of sine or cosine : \(\sin \frac{A}{8} \sin \frac{3 A}{8}\)

Prove that \(\frac { sin(-\theta )tan({ 90 }^{ o }-\theta )sec\left( { 180 }^{ o }-\theta \right) }{ sin(180+\theta )cot(360-\theta )cosec({ 90 }^{ o }-\theta ) } =1\)

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 tan \(\alpha={{1}\over{7}},\sin\beta={{1}\over{\sqrt{10}}},\) Prove that \(\alpha+2\beta={{\pi}\over{4}}\) where \(0<\alpha<{{\pi}\over{2}}\) and \(0<\beta<{{\pi}\over{2.}}\)