# Thread: trig equation and identity help.

1. ## trig equation and identity help.

hi guys,

i have a problem with this trig equation.

1)5sinxcosx - sinx = 0

i tried divding this equation with cos turing the equation in terms of tan to solve it , i got tan = 4, but the angles i got didn't match the answer of the book.

2) tan(30 - x) = 2.
in this equation i don't know how to manipulate the range. i know how to do it when you have for example(x - 30 degress),
if say the range is -90 < x > 90
do i just simple do 30-(-90) and 30-90 ?

3) for the third question can someone prove this identity for me pls, i really have trouble proving it

sinxtanx + cosx = secx

2. Originally Posted by llkkjj24
hi guys,

i have a problem with this trig equation.

1)5sinxcosx - sinx = 0

factor ...

$\displaystyle \textcolor{red}{\sin{x}(5\cos{x} - 1) = 0}$

set each factor equal to 0 and solve for x

2) tan(30 - x) = 2.

note that $\displaystyle \textcolor{red}{\tan(-\theta) = -\tan{\theta}}$

3) for the third question can someone prove this identity for me pls, i really have trouble proving it

sinxtanx + cosx = secx

change tanx to sinx/cosx , get a common denominator, and add the two terms on the left side.
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