What is the value of cos 15°?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The value of cos 15° is (√3 + 1) / (2√2). The value of cos 15° can be calculated using trigonometric identities. Trigonometric functions, such as sine, cosine, and tangent, have values for various angles, and there are mathematical equations called trigonometric identities which relate these values. These identities are helpful for establishing relationships, deriving solutions to trigonometric equations, and simplifying expressions.
Table of content
Value of cos 15°
To calculate the value of cos 15°, we need to determine the value of cos 15° by applying the identity, cos (A – B).
Expressing cos 15° = cos (45° – 30°) ——- (1)
Applying the formula cos (A – B) = cos A. cos B + sin A. sin B
cos (45° – 30°) = cos 45°. cos 30° + sin 45°. sin 30° ——- (2)
We know that sin 45° = 1/√2, cos 45° = 1/√2, sin 30° = 1/2, cos 30° = √3/2
By substituting the values of sin 30°, sin 45°, cos 30°, and cos 45°, equation (2) becomes
cos (45° – 30°) = (1/√2) * (√3/2) + (1/√2) * (1/2)
cos 15° = (√3/2√2) + (1/2√2)
cos 15° = (√3 + 1) / (2√2)
Therefore, the value of cos 15° is (√3 + 1) / (2√2).
Summary
What is the value of cos 15°?
The value of cos 15° is (√3+1) / 2√2. Moreover, cos 15° can be written as 0.965 or (√3+1) / 2√2.
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