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.

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TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Trigonometric Functions" — 8 important questions with detailed answers for CBSE bo…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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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.
If sin θ = 3/5 and 0 < θ < π/2, find cos θ, tan θ, and sec θ.
Prove that: cos(A + B) = cos A cos B - sin A sin B using the unit circle appr…
Find the period and amplitude of the function f(x) = 3 sin(2x) + 1.
+ 2 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
If sin θ = 3/5 and 0 < θ < π/2, find cos θ, tan θ, and se…	✓ Solved
Prove that: cos(A + B) = cos A cos B - sin A sin B using …	✓ Solved
Find the period and amplitude of the function f(x) = 3 si…	✓ Solved

Showing 6 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 required values. sin(π/6) = 1/2 cos(π/4) = √2/2 tan(π/3) = √3 Final Answer: sin(π/6) = 1/2, cos(π/4) = √2/2, tan(π/3) = √3

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 = sec²θ = RHS ✓ Final Answer: The identity is proved: (sin²θ + cos²θ) / cos²θ = sec²θ

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), where n ∈ ℤ Step 4: Expand for clarity. When n is even (n = 2k): x = 2kπ + π/6, k ∈ ℤ When n is odd (n = 2k + 1): x = (2k + 1)π - π/6 = 2kπ + π - π/6 = 2kπ + 5π/6, k ∈ ℤ Final Answer: x = nπ + (...

Q4: If sin θ = 3/5 and 0 < θ < π/2, find cos θ, tan θ, and sec θ.

Step 1: Given information. sin θ = 3/5, and θ is in the first quadrant (0 < θ < π/2). Step 2: Find cos θ using the Pythagorean identity. sin²θ + cos²θ = 1 (3/5)² + cos²θ = 1 9/25 + cos²θ = 1 cos²θ = 1 - 9/25 = 16/25 cos θ = ±4/5 Since θ is in the first quadrant, cos θ > 0. cos θ = 4/5 Step 3: Find tan θ. tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4 Step 4: Find sec θ. sec θ = 1 / cos θ = 1 / (4/5) = 5/4 Step 5: Verify using another identity. tan²θ + 1 = sec²θ (3/4)² + 1 = (5/4)² 9/1...

Q5: Prove that: cos(A + B) = cos A cos B - sin A sin B using the unit circle approach.

Step 1: Set up points on the unit circle. Let P(A) = (cos A, sin A) be a point at angle A. Let P(B) = (cos B, sin B) be a point at angle B. Let P(A+B) = (cos(A+B), sin(A+B)) be a point at angle A+B. Step 2: Consider the angle between P(A) and P(B). The angle from P(B) to P(A) is A - B. Step 3: Use the distance formula. Distance from P(A) to P(B): P(A)P(B)² = (cos A - cos B)² + (sin A - sin B)² = cos²A - 2cos A cos B + cos²B + sin²A - 2sin A sin B + sin²B = (cos²A + sin²A) + (cos²B + sin²B) - 2...

Q6: Find the period and amplitude of the function f(x) = 3 sin(2x) + 1.

Step 1: Identify the standard form. The function is f(x) = 3 sin(2x) + 1 Compare with: f(x) = A sin(Bx + C) + D Step 2: Extract parameters. Amplitude |A| = |3| = 3 B = 2 C = 0 (phase shift = 0) D = 1 (vertical shift) Step 3: Find the period. Period = 2π / |B| = 2π / 2 = π Step 4: Find the range. The basic sine function sin(2x) oscillates between -1 and 1. Multiplying by 3: 3 sin(2x) oscillates between -3 and 3. Adding 1: 3 sin(2x) + 1 oscillates between -3 + 1 = -2 and 3 + 1 = 4. Range: [-2, ...

Showing 6 of 8 questions. Visit the full page for complete solutions.