Question

For each equation, either prove that it is an identity or give a counterexample that proves it is not. Describe the process you followed. a. ( an (a+b)= an (a)+ an (b) ) b. ( an (x+pi)= an (x) ) c. ( -cos (2 x)=sin ^{4}(x)-cos ^{4}(x) ) d. ( cot (x)-csc (x)=frac{sin (x) cos (x)-sin (x)}{sin ^{2}(x)} )

          For each equation, either prove that it is an identity or give a counterexample that proves it is not. Describe the process you followed.
a. ( 	an (a+b)=	an (a)+	an (b) )
b. ( 	an (x+pi)=	an (x) )
c. ( -cos (2 x)=sin ^{4}(x)-cos ^{4}(x) )
d. ( cot (x)-csc (x)=frac{sin (x) cos (x)-sin (x)}{sin ^{2}(x)} )

$For each equation, either prove that it is an identity or give a counterexample that proves it is not. Describe the process you followed. a. ( an (a+b)= an (a)+ an (b) ) b. ( an (x+pi)= an (x) ) c. ( -cos (2 x)=sin ^4(x)-cos ^4(x) ) d. ( cot (x)-csc (x)=fracsin (x) cos (x)-sin (x)sin ^2(x) )$

Added by David C.

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 6

Instant Answer

Solved by Expert Matthew Wagner

06/14/2023

Step 1

To prove or disprove the equation $ \tan (a+b)=\tan (a)+\tan (b) $, we can use the angle addition formula for tangent: $ \tan (a+b) = \frac{\tan (a) + \tan (b)}{1 - \tan (a) \tan (b)} $ Comparing this with the given equation, we can see that they are not the Show more…

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