Find Value of X--->Trig

[mathxyz]

NOTE: d = degrees

If sec (3x - 10)d = csc (x + 40)d, then a possible value of x is

1) 25

2) 15

3) 55

4) 65

MY WORK:

3x - 10 = x + 40

After doing the algebra, my answer is x = 25, which is choice one above.
The book's answer is x = 15, which is choice 2.

What is the correct method to solve this question? Am I not suppose to solve for x using algebra?

 

[tkhunny]

No good. csc(x) ≠ sec(x), generally. You must get the functions exactly the same before simply extracting their arguments.

sec(3x - 10°) = csc(x + 40°)

Since no one knows anything about secants and cosecants, I'm tempted to get rid of them.

sec(x) = 1/cos(x)
csc(x) = 1/sin(x)

cos(3x - 10°) = sin(x + 40°)

Something else you should know:

cos(x) = sin(90° - x)

sin(90º - (3x - 10°)) = sin(x + 40°)
sin(90º - 3x + 10°) = sin(x + 40°)
sin(100º - 3x) = sin(x + 40°)

OK, now the function are the same. Do the algebra again and see what you get.

 

[mathxyz]

hey

Thanks for your notes. I will continue where you ended.