Math Problem Statement
Solution
Let's break down and solve the question visible in the image.
Given:
- , so
We are asked to find the value of , where .
Step 1: Solve for
We are given: Squaring both sides: Now, using the identity: We know: Thus: Now:
Step 2: Calculate
From earlier, we know: Adding these: Finding a common denominator:
Thus, the value of is .
Answer:
The correct option is (1) .
Would you like more details or have any questions?
Here are five related questions for practice:
- What is the double angle identity for ?
- How do you derive the value of if ?
- What is the value of when ?
- How do you calculate if and are given in terms of radians?
- What is the sum of angles formula for tangent?
Tip: Always use trigonometric identities to simplify expressions before plugging in values.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Algebra
Double Angle Identities
Formulas
tan(2β) = 2tan(β) / (1 - tan²(β))
cos(2β) = 2cos²(β) - 1
tan(α) + tan(β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))
Theorems
Pythagorean Identity
Double Angle Identity
Suitable Grade Level
Grades 11-12
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