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Question
If x = a cos3θ and y = b sin3θ, prove that `(x/a)^(2/3) + (y/b)^(2/3) = 1`.
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Solution
We have x = a `cos^3 theta `
= > `x/a = cos^3 theta ........(i)`
Again, `y = b sin^3 theta`
= > `y/b = sin^3 theta .....(ii)`
Now, LHS = `(x/a)^(2/3) + (y/b)^(2/3)`
= `( cos^3 theta )^(2/3) + (sin^3 theta )^ (2/3 )` [ from (i) and (ii)]
=` cos^2 theta + sin^2 theta `
=1
𝐻𝑒𝑛𝑐𝑒, 𝐿𝐻𝑆 = 𝑅𝐻𝑆
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