Question

5sin2 thita +4cos2 thita =9/2

Answer 1

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Answer 2

Let angle theta = A

Now,
=> 5 sin^2 A + 4 cos^2 A = 9/2
=> 5 sin^2 A + 4( 1 - sin^2 A) = 9/2
=> 5 sin^2 A + 4 - 4 sin^2 A=9/2
=> 5 sin^2 A - 4 sin^2 A + 4 =9/2
=> sin^2 A =(9/2) - 4
=> sin^2 A =(9-8)/2
=> sin^2 A =1/2
=> sin A =root 1/2
=> sin A =1/root 2

Also sin 45 = 1/root 2

Therefore A=45
And theta=45