Question

Given that cos^ 2 theta-sin^ 2 theta= 3/4 . What is the value of cos theta?
A. (sqrt(3))/2
B. 1/2
C. (sqrt(7))/2
D. (sqrt(7))/(sqrt(8)) ن​

Answer 1

Option (D)

Step-by-step explanation:

Given :-

cos² θ - sin² θ = 3/4

To find :-

Value of cos θ

Solution :-

Given that

cos² θ - sin² θ = 3/4

We know that

sin² θ + cos² θ = 1

=> sin² θ = 1 - cos² θ

Now,

cos² θ - ( 1 - cos² θ ) = 3/4

=> cos² θ - 1 + cos² θ = 3/4

=> 2 cos² θ - 1 = 3/4

=> 2 cos² θ = (3/4) + 1

=> 2 cos² θ = (3+4)/4

=> 2 cos² θ = 7/4

=> cos² θ = (7/4)/2

=> cos² θ = 7/(4×2)

=> cos² θ = 7/8

=> cos θ = √(7/8)

Therefore, cos θ = √(7/8)

Used formulae:-

→ sin² θ + cos² θ = 1

Answer 2

Step-by-step explanation:

Option (D)

Step-by-step explanation:

Given :-

cos² θ - sin² θ = 3/4

To find :-

Value of cos θ

Solution :-

Given that

cos² θ - sin² θ = 3/4

We know that

sin² θ + cos² θ = 1

=> sin² θ = 1 - cos² θ

Now,

cos² θ - ( 1 - cos² θ ) = 3/4

=> cos² θ - 1 + cos² θ = 3/4

=> 2 cos² θ - 1 = 3/4

=> 2 cos² θ = (3/4) + 1

=> 2 cos² θ = (3+4)/4

=> 2 cos² θ = 7/4

=> cos² θ = (7/4)/2

=> cos² θ = 7/(4×2)

=> cos² θ = 7/8

=> cos θ = √(7/8)

Therefore, cos θ = √(7/8)

Used formulae:-

→ sin² θ + cos² θ = 1

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