Question

Find the value for that makes the statement true: sin = cos( + 40)​

Answer 1

`\boxed{\theta=25}`

Explanation:

I guess the correct equation is something like this:

`\sin( \theta)= \cos(\theta + 40)`

I will use the following trigonometric identity:

`\cos(x+y)=\cos(x) \cos(y)-\sin(x) \sin(y)`

rewriting the equation

`\sin(\theta)=\cos(\theta) \cos(40)-\sin(\theta) \sin(40)\\\sin(\theta)+\sin(\theta) \sin(40)=\cos(\theta) \cos(40)`

common factor:

`\sin(\theta)(1+\sin(40))=\cos(\theta) \cos(40) \\\\(\sin(\theta))/(\cos(\theta))= (\cos(40))/(1+\sin(40)))`

And using also the following identity:

`(\sin(\theta))/(\cos(\theta)) =tan(\theta)`

rewriting the equation

`tan(\theta)= (\cos(40))/(1+\sin(40)))\\\theta= \tan^(-1)((\cos(40))/(1+\sin(40))))\\\theta=25`

By this, we have solved the exercise.

`\text{-B$\mathfrak{randon}$VN}`