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Question
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Solution
Given:
`x = a cos^3 theta`
`=> x/a = cos^3 theta`
`x = b sin^3 theta`
`=> y/b = sin^3 theta`
We have to prove `(x/a)^(2/3) + (y/b)^(2/3) = 1`
We know that `sin^2 theta + cos^2 theta =1`
So we have
`(x/a)^(2/3) + (yb)^(2/3) = (cos^2 theta)^(2/3) + (sin^3 theta)^(2/3)`
`=> (x/a)^(2/3) + (y/b)^(2/3) = cos^2 theta + sin^2 theta`
`=> (x/a)^(2/3) + (y/b)^(2/3) = 1`
Hence proved
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