Question

If x cos theta minus y Sin theta is equal to a and xSin theta + y cos theta is equals to B prove that x square minus y square is equals to a square + b square

Answer 1

Answer:

Let theta = ∅.

Step-by-step explanation:

It is given that x cos∅ - y sin∅ = a

and x sin∅ + y cos ∅ = b

We need to prove x² - y² = a² + b².

Squaring the given equations,

x²cos²∅ + y² sin²∅ - 2 x.y sin∅.cos∅ = a²

and x²sin²∅ + y²cos²∅ + 2 x y sin∅. cos∅ = b²

Adding the above two equations, x²( sin²∅ + cos²∅) + y² (sin²∅ + cos²∅) = a² + b²

We know that sin²∅ + cos²∅ =1

So we get, x² + y² = a² + b²

Hence proved.

Answer 2

Answer:

See the Attachment