Question

if cosx/cosy =a and sinx/siny=b then the value of sin^2 y in terms of a and b?​

Answer 1

Given : cosx/cosy =a and sinx/siny=b

To Find : sin² y in terms of a and b

Solution:

cosx/cosy =a

=> cosx = acosy

=>cos²x = a²cos²y

sinx/siny=b

=>sinx = bsiny

=> sin²x = b²sin²y

cos²x + sin²x  =  a²cos²y + b²sin²y

=> 1 = a²cos²y + b²sin²y

=>  1 = a²(1-sin²y) + b²sin²y

=> 1 = a² - a²sin²y + b²sin²y

=>  1- a² = - a²sin²y + b²sin²y

=> 1  - a² = sin²y (b² - a²)

=>  sin²y = ( 1  - a²)/(b² - a²)

 sin²y = ( 1  - a²)/(b² - a²)

or   sin²y = ( a²-1)/(a² - b²)

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