# Math Help - Trig Equation

1. ## Trig Equation

If you could help with these thanks!

#1) 2sin^2X=sinX

#2) cosX=sinX

#3) tanX+secX=1

2. Originally Posted by amanda0603

#1) 2sin^2X=sinX

$2\sin^2{x} - \sin{x} = 0$

$\sin{x}(2\sin{x} - 1) = 0$

set each factor equal to 0 and solve for x

#2) cosX=sinX

solve this one by looking at your unit circle

#3) tanX+secX=1

$\sec{x} = 1 - \tan{x}$

square both sides ...

$\sec^2{x} = 1 - 2\tan{x} + \tan^2{x}$

$1 + \tan^2{x} = 1 - 2\tan{x} + \tan^2{x}
$

$0 = -2\tan{x}$

solve for x
.

3. Originally Posted by skeeter
.
Alternatively for #2, divide both sides by $\cos{x}$ to give

$1 = \tan{x}$.

Solve for $x$.

4. Originally Posted by Prove It
Alternatively for #2, divide both sides by $\cos{x}$ to give

$1 = \tan{x}$.

Solve for $x$.
o.k. in this particular equation, but not always a good idea in general as $cos{x} = 0$ may be a possible solution in another equation.

5. Originally Posted by amanda0603
If you could help with these thanks!

#1) 2sin^2X=sinX

#2) cosX=sinX

#3) tanX+secX=1
#1) 2sin^2x = sinx
2sin^2x - sinx = 0
sinx (2sinx - 1) = 0
sinx = 0
x = 0, 180, 360

2sinx - 1 = 0
2sinx = 1
sinx = 1/2
x = 30, 150

0verall: 0, 30, 150, 180, 360

#2) cosx = sinx

cosx - sinx = 0
1 - tanx = 0
tanx = 1
x = 45, 225