Question

if 3tan(a-15°) = tan(a+15°) prove that a= 45°

Answer 1

3tan ( a - 15°) = tan( a + 15°)

3/1 = tan( a + 15°)/tan( a - 15°)

use componendo and devedendo rule ,
(3 + 1 )/( 3 - 1) = { tan( a + 15°) + tan(a -15°)}/{ tan( a + 15°) - tan( a -15°)}

2 = { sin(a + 15°).cos(a -15°) + sin(a -15°).cos(a +15°) }/cos(a +15°).cos(a -15°)}/{ sin(a +15°).cos(a - 15°)-sin(a - 15°).cos( a +15°)}/cos(a+15°).cos(a-15°)}

2 = sin( a + 15 + a - 15°)/sin( a +15°-a + 15°)

2 = sin2a/sin30°

2sin30° = sin2a

2 × 1/2 = sin2a

sin2a = 1 = sin90°

2a = 90°

a = 45°

hence proved //