Trigonometric Functions · Question 27

If [- 7 6, 4 3 ], then the number of solutions of 3 cosec2 - 2( 3 - 1) cosec - 4 = 0, is equal to :

1. 7
2. 10
3. 6
4. 8

Answer

(3) 6

Solution

Let cosec = u: 3u2 - 2( 3 - 1)u - 4 = 0

3u2 - 2 3u + 2u - 4 = 0

3u(u - 2) + 2(u - 2) = 0

(u - 2)( 3u + 2) = 0

cosec = 2 or cosec = - 2 3

= 12 or = - 32

In [- 7 6, 4 3 ]:

= 12: = - 7 6, 6, 5 6 (3 values)

= - 32: = - 2 3, - 3, 4 3 (3 values)

number of solutions = 3 + 3 = 6

Answer: (3)