If 3 × tan(x – 15) = tan(x + 15), then the value of x is:

  • a)
    30º

  • b)
    45º

  • c)
    60º

  • d)
    90º

Correct answer is option 'B'. Can you explain this answer?

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Answers

3 × tan (x – 15) = tan (x + 15)
⇒ tan(x + 15) / tan(x – 15) = 3/1
⇒ {tan (x + 15) + tan (x – 15)} / {tan (x + 15) – tan (x – 15)} = (3 + 1) / (3 – 1)
⇒ {tan (x + 15) + tan (x – 15)} / {tan (x + 15) – tan (x – 15)} = 2
⇒ sin(x + 15 + x – 15) / sin(x + 15 – x + 15) = 2
⇒ sin 2x / sin 30 = 2
⇒ sin 2x / (1/2) = 2
⇒ 2 × sin 2x = 2
⇒ sin 2x = 1
⇒ sin 2x = sin 90
⇒ 2x = 90
⇒ x = 45

3 × tan (x – 15) = tan (x + 15)⇒ tan(x + 15) / tan(x – 15) = 3/1⇒ {tan (x + 15) + tan (x – 15)} / {tan (x + 15) – tan (x – 15)} = (3 + 1) / (3 – 1)⇒ {tan (x + 15) + tan (x – 15)} / {tan (x + 15) – tan (x – 15)} = 2⇒ sin(x + 15 + x – 15) / sin(x + 15 – x + 15) = 2⇒ sin 2x / sin 30 = 2⇒ sin 2x / (1/2) = 2⇒ 2 × sin 2x = 2⇒ sin 2x = 1⇒ sin 2x = sin 90⇒ 2x = 90⇒ x = 45
3 × tan (x – 15) = tan (x + 15)⇒ tan(x + 15) / tan(x – 15) = 3/1⇒ {tan (x + 15) + tan (x – 15)} / {tan (x + 15) – tan (x – 15)} = (3 + 1) / (3 – 1)⇒ {tan (x + 15) + tan (x – 15)} / {tan (x + 15) – tan (x – 15)} = 2⇒ sin(x + 15 + x – 15) / sin(x + 15 – x + 15) = 2⇒ sin 2x / sin 30 = 2⇒ sin 2x / (1/2) = 2⇒ 2 × sin 2x = 2⇒ sin 2x = 1⇒ sin 2x = sin 90⇒ 2x = 90⇒ x = 45