Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Differentiate each trigonometric identity to obtain a new (or familiar) identity.(a) $ \tan x = \frac {\sin x}{\cos x} $(b) $ \sec x = \frac {1}{\cos x} $(c) $ \sin x + \cos x = \frac {1 + \cot x}{\csc x} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a) $\sec ^{2} x=\frac{1}{\cos ^{2} x}$b) $\tan x \sec x$c) $\cos x-\sin x=\frac{\cot x-1}{\csc x}$

00:15

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

03:00

Verify each identity.$…

01:09

01:16

Verify that each trigonome…

01:46

03:59

Verify each of the trigono…

Yes, Claire. So when you right here. So we know that the derivative of tan seek it square. So the sequence square gives us co sign. Where is the derivative of sign? Minus sign times the derivative of co sign over. Co sign square. Always simplifying. Get co signed Square signed. Square over. Co sign square and this gives us one over co signed square report Be we're gonna difference She the derivative of secret is equal to seek it. Times tangent We're gonna apply the quotient room, get the co sign, comes the derivative of one my ass One times the derivative of co sign over co sign square. This becomes equal to sign Thanks over co sign square for part C, we have signed X. Let's go Sign is equal to one plus cu o tangent over CO c Good. We're gonna differentiate both sides in respect to X using the quotient rule get co sign of X minus Sign of acts is equal to seek it. Hi. Negative. Cosi can't square minus one plus go to engine times. Negative, but it go seek. It turns court engine all over. Go seek it square it says equal to co sign minus sign is equal to negative Co. C Can't Square Klesko 10 Gin plus coach Engine square over Co Seek it. Wait. Have to use our identity of co Tangent Square is equal to CO C can't square minus one. This becomes equal to we'll sign minus sign. It is equal to this. The cones CO C can't square minus one. So only simplify. I get coat engine My last one over Costa Rican.

View More Answers From This Book

Find Another Textbook

Numerade Educator