Answer:
279/1640
Step-by-step explanation:
The relations between the various trig functions can be used to find the necessary function values.
Other trig functions
Solving for cos(θ), we have ...
41 cos(θ) = 9
cos(θ) = 9/41 . . . . . divide by 41
The Pythagorean relation tells you ...
sin²(θ) +cos²(θ) = 1 ⇒ sin(θ) = √(1 -cos²(θ))
sin(θ) = √(1 -(9/41)²) = (√(41² -9²))/41 = 40/41
The tangent relation is ...
tan(θ) = sin(θ)/cos(θ) = (40/41)/(9/41) = 40/9
Expression value
The value of the given expression is ...
(sin(θ) -cos(θ))/tan(θ) = (40/41 -9/41)/(40/9) = (31/41)(9/40) = 279/1640
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Additional comment
This can also be figured by a suitable calculator or spreadsheet. Output formatted as a fraction is often an option. Here, the result is rational.
