If \(\triangle ABC\) is a right triangle and if \(\angle A=\frac{\pi}{2}\), then prove that \(\cos^2B+\cos^2C=1\)

Find the values of other five trigonometric functions for the following
sin \(\theta\) = -\(\frac { 2 }{ 3 },\) \(\theta\) = lies in the IV quadrant

Prove that \(\sin { 4\alpha } =4\tan { \alpha } \frac { 1-\tan ^{ 2 }{ \alpha } }{ { \left( 1+\tan ^{ 2 }{ \alpha } \right) }^{ 2 } } \)

Express each of the following as a sum or difference. sin 4x cos 2x

Express each of the following as a product.
cos 65^o + cos 15^o

Find the value of sin 150⁰.

Find the values of cos 15⁰.

Simplify: cos A + cos (120° + A) + cos (120° - A)

Find the values of \(sin(-\frac{11\pi}{3})\).

Find the values of other five trigonometric functions for the following
tan \(\theta\) = -2, \(\theta\) lies in the II quadrant