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.

Cos2 theta formula |

Cos 2 theta= 1 – sin2 theta |

**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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