Class 11th Maths – RD Sharma Chapter 8 : Trigonometric Formulae – Exercise 8.2 Solutions (Step-by-Step Guide)

  1. Express each of the following as the product of sines and cosines:

  (i) sin 12x + sin 4x Watch Solution

  (ii) sin 5x − sin x Watch Solution

  (iii) cos 12x + cos 8x Watch Solution

  (iv) cos 12x − cos 4x Watch Solution

  (v) sin 2x + cos 4x Watch Solution

  1. Prove that:

  (i) sin 38° + sin 22° = sin 82° Watch Solution

  (ii) cos 100° + cos 20° = cos 40° Watch Solution

  (iii) sin 50° + sin 10° = cos 20° Watch Solution

  (iv) sin 23° + sin 37° = cos 7° Watch Solution

  (v) sin 105° + cos 105° = cos 45° Watch Solution

  (vi) sin 40° + sin 20° = cos 10° Watch Solution

  1. Prove that:

  (i) cos 55° + cos 65° + cos 175° = 0 Watch Solution

  (ii) sin 50° − sin 70° + sin 10° = 0 Watch Solution

  (iii) cos 80° + cos 40° − cos 20° = 0 Watch Solution

  (iv) cos 20° + cos 100° + cos 140° = 0 Watch Solution

  (v) sin 5π/18 − cos 4π/9 = √3 sin π/9 Watch Solution

  (vi) cos π/12 − sin π/12 = 1/√2 Watch Solution

  (vii) sin 80° − cos 70° = cos 50° Watch Solution

  (viii) sin 51° + cos 81° = cos 21° Watch Solution

  1. Prove that:

  (i) cos (3π/4 + x) − cos (3π/4 − x) = −√2 sin x Watch Solution

  (ii) cos (π/4 + x) + cos (π/4 − x) = √2 cos x Watch Solution

  1. Prove that:

  (i) sin 65° + cos 65° = √2 cos 20° Watch Solution

   (ii) sin 47° + cos 77° = cos 17° Watch Solution

  1. Prove that:

  (i) cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A Watch Solution

  (ii) cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A Watch Solution

  (iii) sin A + sin 2A + sin 4A + sin 5A = 4 cos A/2 cos 3A/2 sin 3A Watch Solution

  (iv) sin 3A + sin 2A − sin A = 4 sin A cos A/2 cos 3A/2 Watch Solution

   (v) cos 20° cos 100° + cos 100° cos 140° − cos 140° cos 200° = −3/4 Watch Solution

  (vi) sin x/2 sin 7x/2 + sin 3x/2 sin 11x/2 = sin 2x sin 5x Watch Solution

  (vii) cos x cos x/2 − cos 3x cos 9x/2 = sin 7x sin 8x Watch Solution

  1. Prove that:

  (i) (sin A + sin 3A)/(cos A − cos 3A) = cot A Watch Solution

  (ii) (sin 9A − sin 7A)/(cos 7A − cos 9A) = cot 8A Watch Solution

  (iii) (sin A − sin B)/(cos A + cos B) = tan (A − B)/2 Watch Solution

  (iv) (sin A + sin B)/(sin A − sin B) = tan (A + B)/2 cot (A − B)/2 Watch Solution

  (v) (cos A + cos B)/(cos B − cos A) = cot (A + B)/2 cot (A − B)/2 Watch Solution

  1. Prove that:

  (i) (sin A + sin 3A + sin 5A)/(cos A + cos 3A + cos 5A) = tan 3A Watch Solution

  (ii) (cos 3A + 2 cos 5A + cos 7A)/(cos A + 2 cos 3A + cos 5A) = (cos 5A)/(cos 3A) Watch Solution

  (iii) (cos 4A + cos 3A + cos 2A)/(sin 4A + sin 3A + sin 2A) = cot 3A Watch Solution

  (iv) (sin 3A + sin 5A + sin 7A + sin 9A)/(cos 3A + cos 5A + cos 7A + cos 9A) = tan 6A Watch Solution

  (v) (sin 5A − sin 7A + sin 8A − sin 4A)/(cos 4A + cos 7A − cos 5A − cos 8A) = cot 6A Watch Solution

  (vi) (sin 5A cos 2A − sin 6A cos A)/(sin A sin 2A − cos 2A cos 3A) = tan A Watch Solution

  (vii) (sin 11A sin A + sin 7A sin 3A)/(cos 11A sin A + cos 7A sin 3A) = tan 8A Watch Solution

  (viii) (sin 3A cos 4A − sin A cos 2A)/(sin 4A sin A + cos 6A cos A) = tan 2A Watch Solution

  (ix) (sin A sin 2A + sin 3A sin 6A)/(sin A cos 2A + sin 3A cos 6A) = tan 5A Watch Solution

  (x) (sin A + 2 sin 3A + sin 5A)/(sin 3A + 2 sin 5A + sin 7A) = (sin 3A)/(sin 5A) Watch Solution

  (xi) (sin (θ + ϕ) − 2 sin θ + sin (θ − ϕ))/(cos (θ + ϕ) − 2 cos θ + cos (θ − ϕ)) = tan θ Watch Solution

  1. Prove that:

  (i) sin α + sin β + sin γ − sin (α + β + γ) = 4 sin (α + β)/2 sin (β + γ)/2 sin (γ + α)/2 Watch Solution

  (ii) cos (A + B + C) + cos (A − B + C) + cos (A + B − C) + cos (−A + B + C) = 4 cos A cos B cos C Watch Solution

  1. If cos A + cos B = 1/2 and sin A + sin B = 1/4 , prove that: tan (A + B)/2 = 1/2 Watch Solution

  2. If cosec A + sec A = cosec B + sec B, prove that: tan A tan B = cot (A + B)/2 Watch Solution

  3. If sin 2A = λ sin 2B, prove that: tan (A + B)/tan (A − B) = (λ + 1)/(λ − 1) Watch Solution

  4. Prove that:

  (i) [cos (A + B + C) + cos (−A + B + C) + cos (A − B + C) + cos (A + B − C)] / [sin (A + B + C) + sin (−A + B + C) + sin (A − B + C) − sin (A + B − C)] = cot C Watch Solution

  (ii) sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0 Watch Solution

  1. If cos (A − B)/cos (A + B) + cos (C + D)/cos (C − D) = 0, prove that tan A tan B tan C tan D = −1 Watch Solution

  2. If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ Watch Solution

  3. If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ Watch Solution

  4. If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0 Watch Solution

  5. If x cos θ = y cos (θ + 2π/3) = z cos (θ + 4π/3), prove that xy + yz + zx = 0 Watch Solution

  6. If m sin θ = n sin (θ + 2α), prove that tan (θ + α) cot α = (m + n)/(m − n). Watch Solution

 

Chapter 8: Transformation Formulae – R. D. Sharma Class 11th Maths

  1. Transformation Formulae Exercise 8.1 Video Solution

  2. Transformation Formulae Exercise 8.2 Video Solution

  3. Transformation Formulae Multiple Choice Questions (MCQs) Video Solution Video Solution

  4. Transformation Formulae Fill in the Blanks (FBQs) Video Solution

  5. Transformation Formulae Very Short Answer Questions (VSAQs) Video Solution Video Solution

 

 

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