Question

solve plz..

cos^2 theta- sin theta=1/4

Answer 1

Solution :

{ => Using 'a' in place of theta. }

cos²a-sina = 1/4

(1-sin²a) - sina = 1/4

4-4sin²a-4sina-1 = 0

=> 4sin²a+4sina-3 = 0

=> 4sin²a+6sina-2sina-3 = 0

=> 2sina(2sina+3)-1(2sina+3) = 0

=> (2sina-1)(2sina+3) = 0

since, Sina = -3/2 is not possible

=> Sina = 1/2

=> a = π/6 or 30° Ans.

Answer 2

Answer:

1/2

Step-by-step explanation:

we know that

cos^2 θ -sin θ=1

ie:

1-sin^2 θ-sin θ=1/4

4-4sin^2 θ-4sin  θ-1=0

4sin^2 θ+4sin  θ-3=0

factorizing the above eqn

 (2sin θ+3)(2sin θ-1)=0

θ=-3/2 or θ=1/2 (neglect - value)

   so that sin θ=1/2