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if x= asin theta+ bcos theta and y= acos theta - bsin theta, show that x^2-y^2= a^2 + b^2

if x= asin theta+ bcos theta and y= acos theta - bsin theta, show that x^2-y^2= a^2 + b^2

Grade:10

1 Answers

Ajay
209 Points
6 years ago
$ x = a sin \theta + bcos\theta \\ y = a cos \theta - bsin\theta \\ \\ x^2 = a^2sin^2\theta+b^2cos^2\theta + 2absin\theta cos\theta \\y^2 = a^2cos^2\theta+b^2sin^2\theta - 2absin\theta cos\theta \\ x^2 + y^2 = a^2+b^2$

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