To Explain: How the given figure proves the given expression.
Answer to Problem 56E
It has been explained how the given figure proves the given expression.
Explanation of Solution
Given:
The expression:
The figure:
Concept used:
Tangent value of an angle is the ratio of the length of perpendicular to the length of base.
Calculation:
The given figure consists of small uniform squares.
Let the length of a side of a square be
Then, the length of a diagonal of such a square is
In
Then, by definition,
Put
Simplifying,
On further simplification,
Similarly, in
Then, using the Pythagoras Theorem,
Put
So,
Also, by definition,
Put
Simplifying,
On further simplification,
Finally, in
Then, using the Pythagoras Theorem,
Put
So,
Also, by definition,
Put
Simplifying,
On further simplification,
Now, it can be seen from the figure that,
Now,
Put
This shows how the given figure proves the given expression.
Conclusion:
It has been explained how the given figure proves the given expression.
Chapter 3 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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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