9) The exact value of the secant function is 8√55 / 55.
10) The trigonometric expression cos x / sec x - cot x / tan x is equivalent to the trigonometric expression - cos² x · cot² x.
How to analyze trigonometric functions
Herein we must make use of properties of trigonometric functions and trigonometric equations. 9) In accordance to the statement, the secant function must be positive and the exact value of the function by using trigonometic formulas:
sec A = 1 / cos A = 1 / √(1 - sin² A)
sec A = 1 / √[1 - (- 3 / 8)²]
sec A = 8√55 / 55
The exact value of the secant function is 8√55 / 55.
10) We need to convert a trigonometric expression into another by algebraic and trigonometric means:
cos x / sec x - cot x / tan x
cos x / (1 / cos x) - (cos x / sin x) / (sin x / cos x)
cos² x - cos² x / sin² x
cos ² x · (1 - 1 / sin² x)
cos² x · [(sin² x - 1) / sin² x]
cot² x · (- cos² x)
- cos² x · cot² x
The trigonometric expression cos x / sec x - cot x / tan x is equivalent to the trigonometric expression - cos² x · cot² x.
To learn more on trigonometric expressions: https://brainly.com/question/10083069
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