Class 11th Maths – RD Sharma Chapter 5 : trigonometric Functions Exercise 5.1 Solutions

1. Prove the following identity : sec⁴x – sec²x = tan⁴x + tan²x Watch Solution
2. Prove the following identity : sin⁶x + cos⁶x = 1 – 3 sin²x cos²x  Watch Solution
3. Prove the following identity : (cosec x – sin x) (sec x – cos x) (tan x + cot x) = 1 Watch Solution
4. Prove the following identity : cosec x (sec x – 1) – cot x(1 – cos x) = tan x – sin x Watch Solution
5. Prove the following identity : [(1 – sin x cos x) / {cos x (sec x – cosec x)}] · [(sin²x – cos²x) / (sin³x + cos³x)] = sin x Watch Solution
6. Prove the following identity : tan x/(1 – cot x) + cot x/(1 – tan x) = (sec x cosec x + 1) Watch Solution
7. Prove the following identity : (sin³x + cos³x) / (sin x + cos x) + (sin³x – cos³x) / (sin x – cos x) = 2 Watch Solution
8. Prove the following identity : (sec x sec y + tan x tan y)² – (sec x tan y + tan x sec y)² = 1 Watch Solution
9. Prove the following identity : cos x/(1 – sin x) = (1 + cos x + sin x)/(1 + cos x – sin x) Watch Solution
10. Prove the following identity : tan³x / (1 + tan²x) + cot³x / (1 + cot²x) = (1 – 2 sin²x cos²x) / (sin x cos x) Watch Solution
11. Prove the following identity : 1 – [sin²x / (1 + cot x)] – [cos²x / (1 + tan x)] = sin x cos x Watch Solution
12. Prove the following identity : [1 / (sec²x – cos²x) + 1 / (cosec²x – sin²x)] sin²x cos²x = (1 – sin²x cos²x) / (2 + sin²x cos²x) Watch Solution
13. Prove the following identity : (1 + tan α tan β)² + (tan α – tan β)² = sec²α sec²β Watch Solution
14. Prove the following identity : [(1 + cot x + tan x)(sin x – cos x)] / (sec³x – cosec³x) = sin²x cos²x Watch Solution
15. Prove the following identity : (2 sin x cos x – cos x) / (1 – sin x + sin²x – cos²x) = cot x Watch Solution
16. Prove the following identity : cos x (tan x + 2) (2 tan x + 1) = 2 sec x + 5 sin x Watch Solution
17. If a = 2 sin x/(1+ cos x + sin x), then prove that (1 – cos x + sin x)/(1 + sin x) is also equal to a. Watch Solution
18. If sin x = (a² – b²) / (a² + b²), find the values of tan x, sec x and cosec x Watch Solution
19. If tan x = b/a, then find the value of √(a+b)/(a-b) + √(a-b)/(a+b). Watch Solution
20. If tan x = a/b, show that (a sin x – b cos x) / (a sin x + b cos x) = (a² – b²) / (a² + b²) Watch Solution
21. If cosec x – sin x = a³, sec x – cos x = b³, then prove that a²b²(a² + b²) = 1 Watch Solution
22. If cot x (1 + sin x) = 4m and cot x (1 – sin x) = 4n, prove that (m² – n²)² = mn. Watch Solution
23. If sin x + cos x = m, then prove that sin⁶x + cos⁶x = [4 – 3(m² – 1)²] / 4, where m² ≤ 2 Watch Solution
24. If a = sec x – tan x and b = cosec x + cot x, then show that ab + a – b + 1 = 0 Watch Solution
25. Prove that : |√{(1-sin x)/(1+sin x)} + √{(1+sin x)/(1-sin x)}| = -2/cos x, where π/2 < x < π Watch Solution
26. If Tn = sin^n x + cos^n x, prove that (T3 – T5)/T1 = (T5 – T7)/T3 Watch Solution
27. If Tn = sin^n x + cos^n x, prove that 2T6 – 3T4 + 1 = 0 Watch Solution
28. If Tn = sin^n x + cos^n x, prove that 6T10 – 15T8 + 10T8 + 10T6 – 1 = 0 Watch Solution

Chapter 5: Trigonometric Functions – R. D. Sharma Class 11th Maths

1. Trigonometric Functions Exercise 5.1 Video Solution

2. Trigonometric Functions Exercise 5.2 Video Solution

3. Trigonometric Functions Exercise 5.3 Video Solution

4. Trigonometric Functions Multiple Choice Questions (MCQs) Video Solution Video Solution

5. Trigonometric Functions Fill in the Blanks (FBQs) Video Solution

6. Trigonometric Functions Very Short Answer Questions (VSAQs) Video Solution Video Solution