trigonometry is giving me grief!

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sinx/cos x= tanx

tan x= sin(30)

How did you get to tanx = sin(30) ?

"Find the general solution of the equation sin(x+30)=cosx"

Haven't done maths in about 2 months and I think it may need some new identities that I don't know :/ can anyone help please?

"Find the general solution of the equation sin(x+30)=cosx"

Haven't done maths in about 2 months and I think it may need some new identities that I don't know :/ can anyone help please?

"Find the general solution of the equation sin(x+30)=cosx"

Haven't done maths in about 2 months and I think it may need some new identities that I don't know :/ can anyone help please?

I would say that the simplest version, once you know the sin(A+B)=sinAcosB+cosAsinB identity,

is to use that identity to expand the left hand side then divide by cos x. This will give you an equation of the form tanx = number.

I wrote lists of trigonometric formulae and how to internalize them efficiently a long while ago which you might wish to go through:

Trigo Formulae 1

Trigo Formulae 2

Hope they are useful for your revision. Peace.

Actually if you clicked on the individual image, it should enlarge itself accordingly. Peace.

Peace.

to divide by an unknown value (cos x, that maybe even zero) is critical, you have to
exclude this value. So at the end of solution you have to examine cosx =0

You don't need to check cos x = 0 for this equation since every term contains either sin x or cos x. These cannot both be 0 for the same value of x and so dividing by cos x does not lead to any problems with this pattern of equation.

That is the check in this question

I don't think so


to divide by an unknown value (cos x, that maybe even zero) is critical, you have to
exclude this value. So at the end of solution you have to examine cosx =0

Another method

$\displaystyle \sin\left (x+30\right )=\sin \left (90-x\right )$

that is
$\displaystyle x+30=90-x +k\cdot 360$

or

$\displaystyle x+30=180-(90-x) +k\cdot 360$

The solutions come from the first equation

$\displaystyle 2 x=60 +k\cdot 360$
$\displaystyle x=30 +k\cdot 180$