# ​If tan o = 2mn / m2 - n2 , find the values of the other T-ratios

Dear Student,

Given :  tan $\mathrm{\theta }$  =

We know :  tan $\mathrm{\theta }$$\frac{\mathrm{Opposite}}{\mathrm{Adjacent}}$, So Opposite = 2 m n  and Adjacent = m2 - n2

From Pythagoras theorem we know :

Hypotenuse 2 = Adjacent2 + Opposite2

Hypotenuse2 = ( m2 - n2 )2 + ( 2 m n )2

Hypotenuse2 = m4 + n4  - 2  m2  n2 + 4 m2  n2

Hypotenuse2 = m4 + n4 + 2 m2  n2

Hypotenuse2 = ( m2 +  n2 )2

Hypotenuse = ( m2 +  n2 )

We know :  Cos $\mathrm{\theta }$$\frac{\mathrm{Adjacent}}{\mathrm{Hypotenuse}}$ , So Cos $\mathrm{\theta }$

And

Sec $\mathrm{\theta }$$\frac{\mathrm{Hypotenuse}}{\mathrm{Adjacent}}$ , So Sec $\mathrm{\theta }$

And

Sin $\mathrm{\theta }$$\frac{\mathrm{Opposite}}{\mathrm{Hypotenuse}}$ , So Sin $\mathrm{\theta }$  =

And
Cosec $\mathrm{\theta }$$\frac{\mathrm{Hypotenuse}}{\mathrm{Opposite}}$ , So Cosec $\mathrm{\theta }$  =

And

Cot $\mathrm{\theta }$$\frac{\mathrm{Adjacent}}{\mathrm{Opposite}}$  Cot $\mathrm{\theta }$ =