Question

Find the value of cos2 theta if 2sin2theta =root3

Answer 1

hello users .....

solution:-
we know that;
the value of sin60° = √3/2
and
cos θ = √(1- sin² θ)

here,
@ccording to given;
2 sin 2θ = √3

=> sin 2θ = √3/2

first method to solve,

=> sin 2θ = √3/2
=> sin 2θ = sin 60°
=> 2θ = 60°

here,
cos 2θ = cos 60° = 1/2 Answer

second method to solve,

=> sin 2θ = √3/2

=> cos 2θ = √{ 1 - (√3/2)² }

=> cos 2θ = √ (1 - 3/4)

=> cos 2θ = √{ (4-3)/4 } ....taking LCM....

=> cos 2θ = √1/4

=> cos 2θ = 1 /√4 = 1 / 2 Answer

⭐✡ hope it helps ✡⭐