Concept explainers
For the angles α and β in the figures, find cos(α + β).
To find: The exact value of expression
Answer to Problem 4T
The value of
Explanation of Solution
Formula used:
The product sum formula
Calculation:
From the given figures for the first triangle , let the hypotenuse be x.
Using Pythagoras theorem the value of x is as follows.
Therefore, hypotenuse of the first triangle is
Similarly for the second triangle the base be y.
Using Pythagoras theorem the base is calculated as follows.
Therefore, for the second triangle the base is
Using sum-product formula the value of
From the figure obtain the value of
Similarly obtain the value of sin
Using the first triangle obtain the value of sin
Similarly, obtain the value of cos
Use above values in sum-difference formula and proceed as follows.
Therefore,
Chapter 7 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning