Cos Square theta Formula

The function of an angle i.e the angles and sides relationships is given by trigonometric functions. Sine, cosine, tangent, cotangent, Cos, Cosec are the trigonometric functions. We have different trigonometric values for these trigonometric functions for various angles like 30 ⁰_, 60⁰ etc.

To classify the trigonometric functions, the angles of Sine, cosine and tangent are the primary ones.

Examples of Cos squared theta formula

Question: What is the value of cos square x, if Sin x = ⅗?

Solution: Cos ² x = 1 – Sin² x

= 1 – (⅗)²

= 1 – 9/25

= (25 – 9) / 25

= 16/25

Cos x = 4/5

Question 2: If sin A = 7/25, then find cos²A and cos²A – sin²A.

Solution:
Given,
sin A = 7/25
We know that,
cos²A = 1 – sin²A
= 1 – (7/25)²
= 1 – 49/625
= (625 – 49)/625
= 576/625
Therefore, cos²A = 576/625
Now,
cos²A – sin²A = (576/625) – (49/625)
= 527/625

Question 3: If cos²x – sin²x = 41/841, then find the value of cos²x.

Solution:
Given,
cos²x – sin²x = 41/841
Substituting sin²x = 1 – cos²x in the above equation,
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

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