\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

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

\(\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA } \) is

If tan A = \(\frac { a }{ a+1 } \) and B = \(\frac { 1 }{ 2a+1 } \) then the value of A + B is ___________

cos p = \(\frac { 1 }{ 7 } \) and cos Q = \(\frac { 13 }{ 14 } \) where P, Q are angles, then P-Q is _______________

Find the value of tan \(\frac{7\pi}{12}\).

Prove that \(\sin { \left( \pi +\theta \right) } =-\sin { \theta } \)

If cos A = \(\frac { 4 }{ 5 } \), cos B = \(\frac { 12 }{ 13 } ,\frac { 3\pi }{ 2 } \)\(\pi \), find cos(A + B)

Prove that \(\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x } \)

In a ΔABC if a = 3, b = 5 and c = 7, find cos A and cos B.

If sin A = \(\frac{3}{5}\) and cos B = \(\frac{9}{41}\), 0 < A < \(\frac{\pi}{2}\), 0 < B < \(\frac{\pi}{2}\). Find the value of sin (A + B)

Find cos(x - y), given that cos x = \(-\frac{4}{5}\) with \(\pi<x<{{3\pi}\over{2}}\) and \(sin \ y = -{{24}\over{25}}\) with \(\pi<x<{{3\pi}\over{2}}\). 

If a cos \(\theta\) - b sin \(\theta\) = c, show that a sin \(\theta\) + b cos \(\theta\) = \(\pm \sqrt { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } } \)

Prove that cos \(\left( {{3\pi}\over{4}}+x\right)-cos\left({{3\pi}\over{4}}-x\right)=-\sqrt{2}sin\ x.\)

If \(2cos\theta=x+\frac{1}{x}\) then prove that \(2\theta=\frac{1}{2}(x^2+\frac{1}{x^2})\)

If sin \(\theta\) + cos \(\theta\) = m, show that cos⁶\(\theta\) + sin⁶\(\theta\)  = \(\frac { 4-3({ m }^{ 2 }-1)^{ 2 } }{ 4 } \), where m² \(\le \) 2

Prove that \(sin\frac { \theta }{ 2 } sin\frac { 7\theta }{ 2 } +sin\frac { 3\theta }{ 2 } sin\frac { 11\theta }{ 2 } =sin2\theta sin5\theta \)

If the sides of a \(\triangle\)ABC are a = 4, b = 6, and c = 8, show that \(4\cos { B } +3\cos { C } =2\)

Show that \(\sin ^{ -1 }{ \left( \frac { 12 }{ 13 } \right) } +\cos ^{ -1 }{ \left( \frac { 4 }{ 5 } \right) } +\tan ^{ -1 }{ \left( \frac { 63 }{ 16 } \right) } =\pi \)