X-coordinate of Trigonometric Functions (1 Viewer)

[BlueGas]

Can someone explain to me the working out of question 9. a)? When sinx = cosx, why did they divide sinx by cosx? Shouldn't they minus cosx to the other side?

 

[InteGrand]

Can someone explain to me the working out of question 9. a)? When sinx = cosx, why did they divide sinx by cosx? Shouldn't they minus cosx to the other side?

They divided both sides by cos x so that they could get the equation tan x = 1, which is easy to solve. Subtracting cos x from both sides wouldn't really help as much with solving the equation.

 

[BlueGas]

They divided both sides by cos x so that they could get the equation tan x = 1, which is easy to solve. Subtracting cos x from both sides wouldn't really help as much with solving the equation.

Are you actually allowed to do that? Because when it comes to normal algebra you would usually minus to find x.

 

[integral95]

Are you actually allowed to do that? Because when it comes to normal algebra you would usually minus to find x.

Best to do that when there are squares involved such as

 

[braintic]

Are you actually allowed to do that? Because when it comes to normal algebra you would usually minus to find x.

In solving (x-1)² = 2(x-1), you CAN'T divide by (x-1) because x=1 is a zero of BOTH the LHS and RHS, and hence a solution of the equation, so that solution is lost in doing the division.

When solving sinx = cosx, you CAN divide by cosx because there are NO values of x for which sinx and cosx are BOTH zero.
So even though the zeros of cosx will lost by dividing, those zeros won't be solutions of the equation.