Cos Square theta Formula

VIKASH KUMAR SAH
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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 0600 etc.

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

Cos2 theta formula
Cos 2 theta= 1 – sin2 theta

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

 

VIKASH KUMAR SAH
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