Question

if x cos theta - y cos theta = a and x sin theta + y cos theta = b then find value of x² + y²?​ ( ans is $a^{2} + b^{2}$ but how?)

Answer 1

Given:   x Cosθ   - y Sinθ   = a  , x Sinθ  + y Cosθ   =   b

To find : value of x² + y²

Solution:

Correct Question is

x Cosθ   - y Sinθ   = a

x Sinθ  + y Cosθ   =   b

x Cosθ   - y Sinθ   = a

Squaring both sides

=> (x Cosθ   - y Sinθ)²   = a

=> x²Cos²θ  + y²Sin²θ - 2xyCosθSinθ  = a²

=> x²Cos²θ  + y²Sin²θ -  xySin2θ  = a²

x Sinθ  + y Cosθ   =   b

Squaring both sides

=> (x Sinθ   - y Cosθ)²   = b

=> x²Sin²θ  + y²Cos²θ + 2xySinθCosθ  = b²

=>  x²Sin²θ  + y²Cos²θ + xySin2θ  = b²

Adding both

x²Cos²θ  + y²Sin²θ -  xySin2θ +  x²Sin²θ  + y²Cos²θ + xySin2θ  =  a²  + b²

=> x²(Cos²θ + Sin²θ ) + y²(Sin²θ + Cos²θ) =  a²  + b²

=>  x²  + y²  =  a²  + b²

Learn more:

Eliminate θ from x = cot θ + tan θ; y = sec θ - cos θ - Brainly.in

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Answer 2

Answer:

This is actually an answer to your previous question which I had mistakenly wrongly answered.