Cos Square Theta Formula

Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain. Basically, an identity is an equation that holds true for all the values of the variables present in it. The function of an angle i.e the angles and sides relationships is given by trigonometric functions. Sine, cosine, tangent, cotangent, Cos, Cosec are called the trigonometric functions. Let's look into the Cos Square theta formula below.

Formula for Cos Square theta

According to the trigonometric identities, we know that,

cos²θ + sin²θ = 1

where, 

• θ is an acute angle of a right triangle.
• sinθ and cosθ are the trigonometric ratios given as follows:
  sinθ = Altitude/Hypotenuse
  cosθ = Base/Hypotenuse
• sin²θ is the square of sinθ and cos²θ is the square of cosθ i.e,
  sin²θ = (sinθ)²
  cos²θ= (cosθ)²

Thus cos square theta formula is given by,

cos²θ = 1 - sin²θ

Solved Examples using Cos Square Theta Formula

Example 1: What is the value of cos square x, if Sin x = 4/5 ?

Solution:

Using Cos Square theta formula,

Cos ² x = 1 – Sin² x

= 1 – (4/5)²

= 1 – 16/25

= (25 – 16) / 25

= 9/25

Thus, cos x = 3/5

Example 2: If cos²x – sin²x = 41/841, then find the value of cos²x.

Solution:

Given: cos²x – sin²x = 41/841

We know that,

sin²x = 1 – cos²x 

Substituting in the above equation we get,

cos²x – (1 – cos²x) = 41/841

⇒2 cos²x – 1 = 41/841

⇒2 cos²x = 1 + 41/841

⇒2 cos²x = 882/841

⇒cos²x = 882/(841 × 2)

⇒cos²x = 441/841

Thus, the value of cos²x is 441/841.