Question

Please solve this question - Question 8.


Class - X : TRIGONOMETRY

Answer 1

Given :

cos α / cos β = a

==> cos α = a cos β

Squaring both sides we get :

==> cos² α = a² cos²β ...........................(1)

Also :

sin α / sin β = b

sin α = b sin β

Squaring both sides , we get this :

==> sin² α = b² sin² β .............................(2)

Adding (1) and (2) we get :

sin² α + cos² α = a² cos² β + b² sin²β

==> 1 = a² cos² β + b² sin² β [ cos² A + sin² A = 1 ]

We know that : cos² β = 1 - sin² β .

==> 1 = a² ( 1 - sin² β ) + b² sin² β

==> 1 = a² - a² sin² β + b² sin² β

==> 1 - a² = sin² β ( b² - a² )

==> sin² β = ( 1 - a² ) / ( b² - a² )

==> sin² β = ( a² - 1 ) / ( a² - b² )

The right answer is OPTION : C

Hope it helps u bro :-)

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