Question

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

Answer 1

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

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Answer 2

Step-by-step explanation:

here is your answer.....