I still can’t understsnd r formula

That formula is a tool to combine an equation containing the sum or difference of sines and cosines. In some situations, say the equation sin x = cos x, we can divide both sides by cos x to obtain tan x = 1. But what happens if say, sin x - cos x = 0.5? We cannot do the same method. One approach, is then, to use the R-formula to combine the sin x and cos x into a single sin or cos.

You will need to remember the formulae

a sin x + b cos x = R sin (x + alp)
a sin x - b cos x = R sin (x - alp)
a cos x + b sin x = R cos (x - alp)
a cos x - b sin x = R cos (x + alp)

R = sqrt (a2 + b2), essentially Pythagoras theorem

alp = tan-1 (b/a) and must be an acute angle

Depending on which form the question wants you to do, you may need to rearrange the terms.

If the form is R sin (x +- alp), you must put the sin x first before cos x (eg 5 sin x + 2 cos x, not 2 cos x + 5 sin x) as putting the wrong order will get you the wrong order, and hence the wrong angle, for alp.

If the form is R cos (x +- alp), you must put the cos x first before sin x.