Trigonometric F...

$$\left( \text{cosec} { \theta  } -\sin { \theta  }  \right) \left( \sec { \theta  } -\cos { \theta  }  \right) \left( \tan { \theta  } +\cot { \theta  }  \right) $$ simplifies to

If $$\sin \alpha + \cos \alpha = k$$, then $$|\sin \alpha - \cos \alpha |$$ equals.

The expression $$3(\sin x - \cos x)^{4} + 6(\sin x + \cos x)^{2} + 4(\sin^{6}x + \cos^{6}c)$$ is equal to

If $$n = \dfrac {\cos \alpha}{\cos \beta}, m = \dfrac {\sin \alpha}{\sin \beta}$$, then $$(m^{2} - n^{2})\sin^{2}\beta$$ is

$$(\sin \theta + \cos \theta)(1 - \sin \theta \cos \theta)$$ can be written as

$$\sin ^{ 6 }{ \theta  } +\sin ^{ 2 }{ \theta  } \cos ^{ 2 }{ \theta  } -\sin ^{ 4 }{ \theta  } \cos ^{ 4 }{ \theta  } -\cos ^{ 6 }{ \theta  } $$ equals to

$$\left( 1-\sin ^{ 2 }{ \theta  }  \right) \left( 1+\tan ^{ 2 }{ \theta  }  \right) $$ is equal to

$$\cfrac { 3-4\sin ^{ 2 }{ \theta  }  }{ \cos ^{ 2 }{ \theta  }  } $$ is equal to

If $$\tan { \theta  } =\dfrac {3}{4} $$ and $$0<\theta <{ 90 }^{ 0 }$$, then the value of $$\sin { \theta  } \cos { \theta  } $$ is

If $$\cfrac { \sin { \left( x+y \right)  }  }{ \sin { \left( x-y \right)  }  } =\cfrac { a+b }{ a-b } $$, then what is $$\cfrac { \tan { x }  }{ \tan { y }  } $$ equal to?