Question

how to solve sin(theta)=cos(theta)

Answer 1

ok see... whole equation should be equal to 1

Square both sides:

cos²(x) - 2sin(x)cos(x) + sin²(x) = 1

Substitute 1 - sin²(x) for cos²(x):

1 - sin²(x) - 2sin(x)cos(x) + sin²(x) = 1

Combine the like terms and move everything to one side:

-2sin(x)cos(x) = 0

Divide both sides by -2:

sin(x)cos(x) = 0

Set each factor to equal zero:

sin(x) = 0
x = 0, π, 2π

cos(x) = 0
x = π/2, 3π/2

Whenever you square both sides always check your solutions. In this case the solutions π and π/2 DO NOT satisfy the equation so they are not valid solutions.

Answer 2

Wow