# Answer to Question #25320 in Trigonometry for brittany roney

Question #25320

how to find all solutions of cos(x)= sin(x) in the interval [0,2(3.14))

Expert's answer

cos(x)= sin(x)

Let's at first gather all the terms in the left part of the equation:cos(x)-sin(x)=0Now we can multiply both parts of the equation by 1/sqrt(2) in order to transform it into sine of the sum:

1/sqrt(2) * cos(x) - 1/sqrt(2) *sin(x)=0

sin(pi/4)*cos(x)-cos(pi/4)*sin(x)=0Now we have the expression which can be written as a single sine function:

sin( pi/4 -x)=0

pi/4-x=pi*k, k -integer

for our interval we get solution x=pi/4, x=5pi/4

Let's at first gather all the terms in the left part of the equation:cos(x)-sin(x)=0Now we can multiply both parts of the equation by 1/sqrt(2) in order to transform it into sine of the sum:

1/sqrt(2) * cos(x) - 1/sqrt(2) *sin(x)=0

sin(pi/4)*cos(x)-cos(pi/4)*sin(x)=0Now we have the expression which can be written as a single sine function:

sin( pi/4 -x)=0

pi/4-x=pi*k, k -integer

for our interval we get solution x=pi/4, x=5pi/4

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