Concept explainers
(a)
To prove: The identity
(a)
Explanation of Solution
Given information:
The given identity is
Formula Used:
Proof:
Consider the given equation and simplify it.
Further simplify it.
From the above, it is clear that one side of the equation can be transformed into other side of the equation.
Hence, proved.
(b)
To prove: The identity
(b)
Explanation of Solution
Given information:
The given identity is
Formula Used:
Proof:
Consider the left hand side of the given equation and multiply it by the conjugate of the denominator
Split the tangent into the quotient of sine and cosine.
The cosecant is the reciprocal of sine and secant is the reciprocal of cosine.
From the above, it is clear that one side of the equation can be transformed into other side of the equation.
Hence, proved.
(c)
To prove: The identity
(c)
Explanation of Solution
Given information:
The given identity is
Formula Used:
Proof:
Consider the left hand side of the given equation and use Pythagorean identity, which states
Use double angle identity.
From the above, it is clear that one side of the equation can be transformed into other side of the equation.
Hence, proved.
Chapter 7 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- 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