Math Problem Statement
Simplify the trigonometric expressions: 15. sin(x) sec(x) / tan(x), 16. cos(x) sec(x) / cot(x), 17. (sin(t) + tan(t)) / tan(t), 18. (1 + cot(A)) / csc(A).
Solution
Let's simplify the given trigonometric expressions step by step:
15.
- Recall that and .
- Substituting these definitions:
- Simplify the numerator and denominator:
- Cancel out and where appropriate: Answer: 1
16.
- Recall that and .
- Substitute these definitions: [ \frac{\cos x \sec x}{\cot x} =
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Simplification of Trigonometric Expressions
Formulas
sec(x) = 1 / cos(x)
tan(x) = sin(x) / cos(x)
cot(x) = cos(x) / sin(x)
csc(x) = 1 / sin(x)
Theorems
Trigonometric Identities
Suitable Grade Level
Grades 10-12
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