Question

If a cos theta + b sin theta = x and a sin theta
+b cos theta = y, prove that a² + b² = x² + y².
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Answer 1

Error :- It will be a sin theta - b cos theta = y instead of a sin theta + b cos theta = y .

Answer :-

Step-by-step explanation :-

Given :-

→ a cos∅ + b sin∅ = x .

→ a sin∅ - b cos∅ = y .

Now,

We have,

$\because$ x² + y² .

= ( a cos ∅ + b sin ∅ )² + ( a sin∅ - b cos∅ )² .

= a²cos²∅ + b²cos²∅ + 2 ab cos∅ sin∅ + a²sin²∅ + b²sin²∅ - 2 ab sin∅ cos∅ .

= a²cos²∅ + b²cos²∅ + a²sin²∅ + b²sin²∅ .

= a²cos²∅ + a²sin²∅ + b²cos²∅ + b²cos²∅ .

= a²( cos²∅ + sin²∅ ) + b²( cos²∅ + sin²∅ ) .

= a² + b² .

LHS = RHS .

Hence, it is proved .