Question

If x = a sin theta and y = b cos theta ,then prove that x²/a²+y²/b²=1​

Answer 1

Step-by-step explanation:

Given:-

x = a sin theta and y = b cos theta

To find:-

Prove that (x^2/a^2)+(y^2/b^2) = 1

Solution:-

Given equations are:

x = a sin θ

=>x/a = sin θ

On squaring both sides then

=>(x/a)^2 =( sin θ)^2

x^2/a^2 = sin^2 θ--------------(1)

and

y = b cos θ

=>y/b = cos θ

On squaring both sides then

=>(y/b)^2 = (cos θ)^2

y^2/b^2 = cos^2 θ-----------(2)

On adding (1)&(2) then

(x^2/a^2)+(y^2/b^2) = sin^2 θ + cos^2 θ

We know that

sin^2 θ + cos^2 θ = 1

(x^2/a^2)+(y^2/b^2) = 1

Hence, Proved

Used formula:-

• sin^2 θ + cos^2 θ = 1