SOLUTION: Evaluate the expression. tan(90-theta)*tan(theta)*sec(theta) a)1 b)0 c)sec(theta) d)cot(theta) (Homeschooling mother. Any help appreciated. Thank you)

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate the expression. tan(90-theta)*tan(theta)*sec(theta) a)1 b)0 c)sec(theta) d)cot(theta) (Homeschooling mother. Any help appreciated. Thank you)      Log On


   

Question 1103429: Evaluate the expression.
tan(90-theta)*tan(theta)*sec(theta)
a)1
b)0
c)sec(theta)
d)cot(theta)
(Homeschooling mother. Any help appreciated. Thank you)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For acute angles (less than 90 degrees),
you could think of trigonometric functions as trigonometric ratios.
If you draw a right triangle with theta as one of the angles,
the measure of the other acute angle will be 90-theta .

C=180%5Eo-B
tan%28B%29=+AC+%2F+AB= (opposite side) / (adjacent side)
tan%28180%5Eo-B%29=tan%28C%29=AB%2FAC .
So,
tan%28180%5Eo-B%29%2Atan%28B%29=%28AB%2FAC%29%2A%28AC+%2F+AB%29=1
It works for acute angle B from a right triangle,
and it also works for any angle theta ,
so tan%28180%5Eo-theta%29%2Atan%28theta%29=1 , and


NOTE: I did not homeschool my children,
I was not brave enough for that,
but I coached my youngest through an online charter school.