Trigonometric Functions — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Trigonometric Functions" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Trigonometric Functions" — 8 important questions with detailed answers for CBSE bo…
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Key Questions Covered:
- Find the value of sin(π/6), cos(π/4), and tan(π/3) using the unit circle or s…
- Prove the trigonometric identity: (sin²θ + cos²θ) / cos²θ = sec²θ.
- Find the general solution of the equation sin x = 1/2.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the value of sin(π/6), cos(π/4), and tan(π/3) using … | ✓ Solved |
| Prove the trigonometric identity: (sin²θ + cos²θ) / cos²θ… | ✓ Solved |
| Find the general solution of the equation sin x = 1/2. | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the value of sin(π/6), cos(π/4), and tan(π/3) using the unit circle or standard values.
Step 1: Recall standard trigonometric values for special angles.
For angle π/6 (30°):
sin(π/6) = 1/2
cos(π/6) = √3/2
tan(π/6) = 1/√3
For angle π/4 (45°):
sin(π/4) = 1/√2 = √2/2
cos(π/4) = 1/√2 = √2/2
tan(π/4) = 1
For angle π/3 (60°):
sin(π/3) = √3/2
cos(π/3) = 1/2
tan(π/3) = √3
Step 2: Identify ...
Q2: Prove the trigonometric identity: (sin²θ + cos²θ) / cos²θ = sec²θ.
Step 1: Start with the left-hand side.
LHS = (sin²θ + cos²θ) / cos²θ
Step 2: Apply the Pythagorean identity.
We know that sin²θ + cos²θ = 1
Step 3: Substitute.
LHS = 1 / cos²θ
Step 4: Use the definition of secant.
sec θ = 1 / cos θ
Therefore, sec²θ = 1 / cos²θ
Step 5: Compare.
LHS = 1 / cos²θ = ...
Q3: Find the general solution of the equation sin x = 1/2.
Step 1: Identify the principal solution.
We need sin x = 1/2
The principal value is x₀ = π/6 (or 30°)
Step 2: Recall the general solution for sin x = a.
If sin x = sin α, then:
x = nπ + (-1)ⁿ α, where n ∈ ℤ
Step 3: Apply the general solution formula.
For sin x = 1/2 = sin(π/6):
x = nπ + (-1)ⁿ (π/6...
Showing 3 of 8 questions. Visit the full page for complete solutions.