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If X=A `Cos^3 Theta and Y = B Sin ^3 Theta ," Prove that " (X/A)^(2/3) + ( Y/B)^(2/3) = 1.` - Mathematics

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Question

If x=a `cos^3 theta and y = b sin ^3 theta ," 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

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Chapter 8: Trigonometric Identities - Exercises 2

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R.S. Aggarwal Mathematics [English] Class 10
Chapter 8 Trigonometric Identities
Exercises 2 | Q 6

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