Solve #cosx+sinx=2/3# ?
Assuming you meant
there are two answers:
To solve this equation, we have to use trigonometric functions to isolate one of the unknowns and solve for that unknown.
In this case, we will use
Let's first use linear combination of cosine and sine with equal arguments formula to simplify it.
That is, we want to express
A cos x +B sin x in the form C cos (x-D). Note that A is the coefficient of cos x and B is the coefficient of sine x.
To find C use pythagorean formula and to find D we use one of these two formulas
From the given equation A = 1 and B = 1. So let's find C using pythagorean theorem.
To find D we need to first figure out which quadrant x is in and because both cos x and sin x are positive it means that x is in quadrant one.
Now let's use that to solve the problem. That is,
Considering the given condition is
Adding (1) and (2) we get