Question

if tan=b/a then find tha value of sin²​

Answer 1

Answer: $\frac{b^{2} }{a^{2} +b^{2} }$

Step-by-step explanation:

tan x = b/a    when x is an angle and ABC is a right angled triangle where AB=b unit, BC=c unit and CA=a unit.

From Pythagorian theorem,

a²+ b²=c²

and from trigonometry we have,

tan x = height/base = AB/AC = b/a

and sin x = height/hypotenuse

= b/c

= $\frac{b}\sqrt{(a^{2}+b^{2})}}$

So sin² x = $(\frac{b}\sqrt{(a^{2}+b^{2})}})^{2}$ = $\frac{b^{2} }{a^{2} +b^{2} }$