If `sintheta=(a^2=b^2)/(a^2+b^2)` , find the values of other five trigonometric ratios.

Answer

`sin theta =(a^(2)-b^(2))/(a^(2)+b^(2)), cos theta= (2ab )/(a^(2)+b^(2)), tan theta =(a^(2)-b^(2))/(2ab),`
`"cosec " theta =(a^(2)+b^(2))/(a^(2)-b^(2)), sectheta =(a^(2)+b^(2))/(2ab), cot theta =-(2ab)/(a^(2)-b^(2))`

Explanation

In right `Delta ABC, angle B=90^(@) and angle BAC=theta.`
Given : `sin theta =(a^(2)-b^(2))/(a^(2)+b^(2))=(BC)/(AC).`
Let ` BC=(a^(2)-b^(2))and AC =(a^(2)+b^(2)).` Then
`AB^(2)=(AC^(2)-BC^(2))=(a^(2)+b^(2))^(2)-(a^(2)-b^(2))^(2)=4a^(2)b^(2)`
`implies AB=2ab . `
Now , we can find all the T-ratios of `theta`.