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