Question

if x=aSin Q+bSin Q and y= aCos Q-b Sin Q. prove that x²+y²=a²+b²

Answer 1

Answer:

Given: x=asin{\theta}+bcos{\theta} and y=acos{\theta}-bsin{\theta}

Now, x^{2}+y^{2}=(asin{\theta}+cos{\theta})^{2}+(acos{\theta}-bsin{\theta})^{2}

x^{2}+y^{2}=a^{2}sin^{2}{\theta}+b^{2}cos^{2}{\theta}+2absin{\theta}cos{\theta}+a^{2}cos^{2}{\theta}+b^{2}sin^{2}{\theta}-2absin{\theta}cos{\theta}

x^{2}+y^{2}=a^{2}(sin^{2}{\theta}+cos^{2}{\theta})+b^{2}(sin^{2}{\theta}+cos^{2}{\theta})

x^{2}+y^{2}=a^{2}(1)+b^{2}(1)

x^{2}+y^{2}=(a^{2}+b^{2})

Step-by-step explanation: