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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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,
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 .
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