Concept explainers
a.
To prove:
a.
Explanation of Solution
Let
Then
This implies that,
But the sine function is an odd function and hence
Then,
And this gives that,
Substituting
Hence proved
b.
To prove:
b.
Explanation of Solution
Let
Then
This implies that,
But the tan function is an odd function and hence
Then,
And this gives that,
Substituting
Hence proved
c.
To prove:
c.
Explanation of Solution
Draw a right angled triangle with sides 1 unit and x unit as shown in figure below:
Here a and b are the acute angles of the triangle.
Since for a right triangle, the sum of acute angles is
Now consider,
This gives that,
Now consider,
This gives that,
Thus,
d.
To prove:
d.
Explanation of Solution
Draw a right angled triangle with hypotenuse 1 unit and a side x unit as shown in figure below:
Here a and b are the acute angles of the triangle.
Since for a right triangle, the sum of acute angles is
Now consider,
This gives that,
Now consider,
This gives that,
Thus,
e.
To prove:
e.
Explanation of Solution
Draw a right angled triangle with hypotenuse 1 unit and a side x unit as shown in figure below:
Here a and b are the acute angles of the triangle.
Then, the length of the remaining side can be found using the Pythagoras theorem as shown:
Now consider,
This gives that,
Now consider,
This gives that,
Thus, from (1) and (2),
Hence,
Chapter 4 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning