Chapter 7: Q. 17 (page 505)

Use sum, difference, product, or half-angle formulas to find the exact value of the expression cos15 $°$

Short Answer

Expert verified

$\cos 15 ° = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

Step by step solution

Step 1. Rewriting the expression

We know that ,

cos(A-B) = cos(A)cos(B) +sin(A)sin(B)

15 $°$ can be written as 45 $°$ -30 $°$

So,

$\cos 15 ° = \cos (45 ° - 30 °) \cos 15 ° = \cos 45 ° \cos 30 ° + \sin 45 ° \sin 30 °$

Step 2. Calculations

$\cos 15 ° = \cos 45 ° \cos 30 ° + \sin 45 ° \sin 30 ° \cos 15 ° = \frac{1}{\sqrt{2}} \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}} \frac{1}{2} \cos 15 ° = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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Use sum, difference, product, or half-angle formulas to find the exact value of the expression cos15 $°$

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. Calculations

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Use sum, difference, product, or half-angle formulas to find the exact value of the expression cos15°

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Theoretical and Mathematical Physics

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Use sum, difference, product, or half-angle formulas to find the exact value of the expression cos15 $°$