How do you solve #sinx+cosx=1#?
3 Answers
Explanation:
The given equation is equivalent to
This can be written as
The general solution of this equation ls
So,
Having noted that there were 40K viewers for the answers by me,
Hero and Nghi, I think I could invoke more interest by including the
solutions for
cos x, when
For cos x - sin x = 1,
the general solution is
Note the change in the multiple from
For
See x-intercepts as graphical solutions.
Graph on uniform scale for solutions
graph{y-cos x - sin x +1 = 0[-7 7 -3 4]}
Graph on uniform scale for solutions
graph{y-cos x + sin x +1 = 0[-7 7 -3 4]}
See combined graph for solutions
graph{(y- sec x - tan x +1)(y- sec x+ tan x +1)=0[-13 13 -6.5 6.5]}
Explanation:
If
Using the identities:
The equation can be simplified to:
Therefore
The values of
But here
However, since we squared the equation, we need to check all of these answers work in the original equation:
When we get to
This can be written as:
Explanation:
Use trig identity:
We get:
Trig table and unit circle give -->