Determine an exact value of c

Question

cot(4c-pi/4)+tan(2c+pi/4)=0

 

Could someone check my work because there is no answer?

 

cotx=tan(pi/2-x)

x=4c-pi/4

 

pi/2-(4c-pi/4)=-2c-pi/4

-2c=-pi

c=pi/2

Answer 1

This looks good to me. You can check your answer by plugging it into the original equation.

 

cot(4(π/2) - π/4) + tan(2(π/2) + π/4) ?= 0

cot(2π - π/4) + tan(π + π/4) ?= 0

cot(-π/4) + tan(π/4) ?= 0

-1 + 1 = 0  √

 

Your answer is correct!