What is the general solution for cos(x)-sin(x)=0,-pi<= x<= pi ?

The general solution for cos(x)-sin(x)=0,-pi<= x<= pi is x= pi/4 ,x=-(3pi)/4

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cos(x)-sin(x)=0,-pi<= x<= pi

cos (x) - sin (x) = 0, - π \leq x \leq π

x = \frac{π}{4}, x = - \frac{3 π}{4}

Solution steps

cos (x) - sin (x) = 0, - π \leq x \leq π

Rewrite using trig identities

1 - tan (x) = 0

Move

1

to the right side

- tan (x) = - 1

Divide both sides by

- 1

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

Solutions for the range

- π \leq x \leq π

x = \frac{π}{4}, x = - \frac{3 π}{4}

5 - tan^{2} (x) = 4

2 sec^{2} (θ) - 3 = tan^{2} (θ)

sin (π - x) + cos (x) = 0

sin (x) = - sin (2 x)

- 3 = 1 + 4 tan (θ)

What is the general solution for cos(x)-sin(x)=0,-pi<= x<= pi ?
The general solution for cos(x)-sin(x)=0,-pi<= x<= pi is x= pi/4 ,x=-(3pi)/4