Sin theta is equal to x square minus y square upon x square plus y square then find the values of cos theta and tan theta in terms of x and y
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Cosθ = 2xy / (x² + y²) & Tanθ = (x² - y²) / 2xy if Sinθ = (x² - y²)/(x² + y²)
Step-by-step explanation:
Given that
Sinθ = (x² - y²)/(x² + y²)
As we know that
Cos²θ = 1 - Sin²θ
=> Cos²θ = 1 - ( (x² - y²)/(x² + y²) )²
=> Cos²θ = (1 + (x² - y²)/(x² + y²)) (1 - (x² - y²)/(x² + y²) )
=> Cos²θ = (2x²/(x² + y²) ) ( 2y²/(x² + y²))
=> Cos²θ = (2xy / (x² + y²) )²
=> Cosθ = 2xy / (x² + y²)
Tanθ = Sinθ/Cosθ
=> Tanθ = ((x² - y²)/(x² + y²)) / (2xy / (x² + y²))
=> Tanθ = (x² - y²) / 2xy
Learn More:
If sin θ + cos θ = 2 , then evaluate : tan θ + cot θ
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