QQuestion
If cos θ = \frac{x}{\sqrt{x²+y²}} , then prove that x sin θ = y cos θ
✓Answer
Cos θ = \text{x}\over \sqrt{\text{x² + y²}}
base (b) = x
hypotenuse (h) = \sqrt{\text{x² + y²}}
Pythagoras Theorem: p² = h² – b²
or, p² = x² + y² – x²
or, p² = y²
or, p = y
LHS: x sin θ = x \text{y}\over \sqrt{\text{x² + y²}}
= y \text{x}\over \sqrt{\text{x² + y²}}
= y cos θ RHS
Hence, x sin θ = y cos θ proved
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