Introduction to...

$$\sin { { 48 }^{ 0 } } .\sin { 12^{ 0 } } =$$

$$1+cosec\dfrac { \pi }{ 4 } +cosec\dfrac { \pi }{ 8 } +cosec\dfrac { \pi }{ 16 } =$$

$$\frac { \sec { 8A } -1 }{ \sec { 4A } -1 } =$$

Suppose $$I_1 = \displaystyle \int_0^{\pi/2} cos(\pi sin^2x)dx; I_2 =  \displaystyle \int_0^{\pi/2} cos(2\pi sin^2x)dx \,and \, I_3 =  \displaystyle \int_0^{\pi/2} cos(\pi sin x)dx$$ then

$$1+cosec\frac { \pi  }{ 4 } +cosec\frac { \pi  }{ 8 } cosec\frac { \pi  }{ 16 } =$$

If the median of a triangle ABC passing through A is perpendicular AB then tanA + 2tanB = 

$$\left( \frac { 1 }{ { sec }^{ 2 }\theta -{ cos }^{ 2 }\theta  } +\dfrac { 1 }{ cosec^{ 2 }{ \theta -sin }^{ 2 }\theta  }  \right) { sin }^{ 2 }{ \theta \quad cos }^{ 2 }\theta =$$

An angle is increasing at a constant rate. The rate of increase of tan when the angle is $$ \pi /3 $$ is 

$$\dfrac{cos A}{1+sin A} +\dfrac{cos A}{1-sin A} =$$

The value of $$\cfrac { cot{ 54 }^{ 0 } }{ cot36^{ 0 } } +\cfrac { tan{ 20 }^{ 0 } }{ cot{ 70 }^{ 0 } } =$$.