Class 11th Maths – RD Sharma Chapter 5 : trigonometric Functions Exercise 5.3 Solutions

1. 1. Find the values of the following trigonometric ratios:

   (i) sin 5π/3 Watch Solution

   (ii) sin 17π Watch Solution

   (iii) tan 11π/6 Watch Solution

   (iv) cos (−25π/4) Watch Solution

   (v) tan 7π/4 Watch Solution

   (vi) sin 17π/6 Watch Solution

   (vii) cos 19π/6 Watch Solution

   (viii) sin (−11π/6) Watch Solution

   (ix) cosec (−20π/3) Watch Solution

   (x) tan (−13π/4) Watch Solution

   (xi) cos 19π/4 Watch Solution

   (xii) sin 41π/4 Watch Solution

   (xiii) cos 39π/4  Watch Solution

   (xiv) sin 151π/6 Watch Solution

   2. Prove that:

   (i) tan 225° cot 405° + tan 765° cot 675° = 0 Watch Solution

   (ii) sin 8π/3 cos 23π/6 + cos 13π/3 sin 35π/6 = 1/2 Watch Solution

   (iii) cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = 1/2 Watch Solution

   (iv) tan (−225°) cot (−405°) − tan (−765°) cot (675°) = 0 Watch Solution

   (v) cos 570° sin 510° + sin (−330°) cos (−390°) = 0  Watch Solution

   (vi) tan 11π/3 − 2 sin 4π/6 − (3/4) cosec^2 π/4 + 4 cos^2 17π/6 = (3 − 4√3)/2 Watch Solution

   (vii) 3 sin π/6 sec π/3 − 4 sin 5π/6 cot π/4 = 1 Watch Solution

   3. Prove that:

   (i) [cos (2π + x) cosec (2π + x) tan (π/2 + x)] / [sec (π/2 + x) cos x cot (π + x)] = 1 Watch Solution

   (ii) [cosec (90° + x) + cot (450° + x)] / [cosec (90° − x) + tan (180° − x)] + [tan (180° + x) + sec (180° − x)] / [tan (360° + x) − sec (−x)] = 2 Watch Solution

   (iii) [sin (π + x) cos (π/2 + x) tan (3π/2 − x) cot (2π − x)] / [sin (2π − x) cos (2π + x) cosec (−x) sin (3π/2 − x)] = 1 Watch Solution

   (iv) {1 + cot x − sec (π/2 + x)} {1 + cot x + sec (π/2 + x)} = 2 cot x  Watch Solution

   (v) [tan (π/2 − x) sec (π − x) sin (−x)] / [sin (π + x) cot (2π − x) cosec (π/2 − x)] = 1 Watch Solution

   4. Prove that:

   sin^2 (π/18) + sin^2 (π/9) + sin^2 (7π/18) + sin^2 (4π/9) = 2 Watch Solution

   5. Prove that:

   sec (3π/2 − x) sec (x − 5π/2) + tan (5π/2 + x) tan (x − 3π/2) = −1 Watch Solution

   6. In a ΔABC, prove that:

   (i) cos (A + B) + cos C = 0 Watch Solution

   (ii) cos [(A + B)/2] = sin (C/2) Watch Solution

   (iii) tan [(A + B)/2] = cot (C/2) Watch Solution

   7. If A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that:

   cos (180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0 Watch Solution

   8. Find x from the following equations:

   (i) cosec (π/2 + θ) + x cos θ cot (π/2 + θ) = sin (π/2 + θ) Watch Solution

   (ii) x cot (π/2 + θ) + tan (π/2 + θ) sin θ + cosec (π/2 + θ) = 0 Watch Solution

   9. Prove that:

   (i) tan 4π − cos 3π/2 − sin 5π/6 cos 2π/3 = 1/4 Watch Solution

   (ii) sin 13π/3 sin 8π/3 + cos 2π/3 sin 5π/6 = 1/2 Watch Solution

   (iii) sin 13π/3 sin 2π/3 + cos 4π/3 sin 13π/6 = 1/2 Watch Solution

   (iv) sin 10π/3 cos 13π/6 + cos 8π/3 sin 5π/6 = −1 Watch Solution

   (v) tan 5π/4 cot 9π/4 + tan 17π/4 cot 15π/4 = 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