Question

if tan A=b/a where a and b are real numbers find the value of sin^2A

Answer 1

Hope this is helpful

Answer 2

Answer:

$Sin^{2} A = \frac{b^2}{b^2+a^2}$

Step-by-step explanation:

$Tan \theta = \frac{Perpendicular}{Base}$

We are given that $Tan A = \frac{b}{a}$

On Comparing

Perpendicular = b

Base = a

Use Pythagoras theorem to find hypotenuse

$Hypotenuse^2=Perpendicular^2+Base^2$

$Hypotenuse^2=b^2+a^2$

$Hypotenuse=\sqrt{b^2+a^2}$

$Sin \theta = \frac{Perpendicular}{hypotenuse}$

$Sin A = \frac{b}{\sqrt{b^2+a^2}}$

Squaring both sides

$Sin^{2} A = \frac{b^2}{b^2+a^2}$

Hence the value of $Sin^{2} A = \frac{b^2}{b^2+a^2}$