Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![**Prove the identity.**
\[
\sin\left(x - \frac{\pi}{2}\right) = -\cos(x)
\]
**Use the Subtraction Formula for Sine, and then simplify:**
\[
\sin\left(x - \frac{\pi}{2}\right) = \left(\sin(x)\right)\left(\cos\left(\frac{\pi}{2}\right)\right) - \left(\cos(x)\right)\left( \right)
\]
\[
= \left(\sin(x)\right)(0) - \left(\cos(x)\right)\left( \right)
\]
\[
= \boxed{}
\]
In the above derivation, each step involves filling in the blanks to complete the identity using trigonometric properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90e413d6-0f95-45bc-9120-3de888a1b336%2F8cd9c927-ef26-478a-932b-ba88b0768d3a%2Fcfzhdgm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Prove the identity.**
\[
\sin\left(x - \frac{\pi}{2}\right) = -\cos(x)
\]
**Use the Subtraction Formula for Sine, and then simplify:**
\[
\sin\left(x - \frac{\pi}{2}\right) = \left(\sin(x)\right)\left(\cos\left(\frac{\pi}{2}\right)\right) - \left(\cos(x)\right)\left( \right)
\]
\[
= \left(\sin(x)\right)(0) - \left(\cos(x)\right)\left( \right)
\]
\[
= \boxed{}
\]
In the above derivation, each step involves filling in the blanks to complete the identity using trigonometric properties.
Expert Solution
Step 1
Given that,
We have to prove this identity.
We know that,
The substraction formula is,
sin(A - B) = sinA cosB - cosA sinB
Step by step
Solved in 2 steps
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