Math Problem Statement
Find the exact value of each of the following: (a) sin 75°, (b) tan 105°, (d) sin 15° cos 15°, (e) tan 22.5°.
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Exact Trigonometric Values
Angle Sum and Difference Identities
Formulas
sin(A ± B) = sin A cos B ± cos A sin B
tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)
tan(A/2) = ±√((1 - cos A) / (1 + cos A))
Theorems
Trigonometric Angle Sum and Difference Identities
Half-Angle Formula for Tangent
Suitable Grade Level
Grades 10-12