Math Problem Statement
Triangle ABC <b= 90° , tan A= 1/√3 . Show that Cos A/1-tan A + sin A/1-Cot A = Sin A+ Cos A
Solution
We are given the following information about a right-angled triangle ABC:
- ∠B = 90° (so, triangle ABC is a right-angled triangle).
- .
We need to show that:
Step 1: Use the trigonometric identity for
We know that:
It is given that:
So, we can find and . Since , we know that:
Step 2: Find
Step 3: Substitute , , , and into the equation
We need to evaluate:
Substituting the known values of , , , and :
- For the first term:
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right-angled triangles
Trigonometric identities
Formulas
tan A = sin A / cos A
cot A = 1 / tan A
Basic trigonometric identities
Theorems
Relationship between sine, cosine, and tangent in right-angled triangles
Trigonometric simplification
Suitable Grade Level
Grades 9-12
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