Question

. If sin 0
a² – b²
a² +b²
find the values of all T-ratios of 0.​

Answer 1

Answer:

hi

Step-by-step explanation:

We have,

sin A = HypotenusePerpendicular​=a2+b2a2−b2​

So, we draw a right triangle right angled at B such that

Perpendicular = a2−b2 and, Hypotenuse = a2+b2. and ∠BAC=θ

By Pythagoras theorem, we have

AC2=AB2+BC2

⇒AB2=(a2+b2)2−(a2−b2)2

⇒AB2=(a4+b4+2a2b2)−(a4+b4−2a2b2)

⇒AB2=4a2b2=(2ab)2

⇒AB=2ab

When we consider the trigonometric ratios of ∠BAC=θ  , we have

Base = AB = 2ab, Perpendicular = BC = a2−b2, and Hypotenuse = AC = a2+b2

∴cosθ=Hypotenuse/Base​=a2+b2/2ab​

⇒tanθ=Base/Perpendicular​=2ab/a2−b2​

⇒cosecθ=Perpendicular/Hypotenuse​=a2−b2/a2+b2​

⇒secθ=Base/Hypotenuse​=2ab/a2+b2​

and,

cotθ=Perpendicular/Base​=a2−b2/2ab​