Question

if x= a cos theta +b sin theta , and y =a sin theta - b cos theta , prove that x^2 + y^2 = a^2 +b^2.​

Answer 1

Answer :-

Step-by-step explanation :-

We have,

→ x = acosθ + bsinθ.

→ y = asinθ - bcosθ.

Now,

→ Squaring both sides and adding the result, we get

→ x² + y² = (acosθ + bsinθ)² + (asinθ - bcosθ)².

       

= a²cos²θ + b²sin²θ + 2abcosθ sinθ + a²sin²θ + b²cos²θ - 2abcosθ sinθ.

= a²(cos²θ + sin²θ) + b²(sin²θ +cos²θ).

= a² + b². [ $\because$ sin²θ +cos²θ = 1 . ]

RHS = LHS

Hence, it is proved.

Answer 2

Answer:

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