Number of solutions of 2 s i n ( | x | ) = 3 | c o s x | in [ − π , π ] , is equal to

Step-by-step solution

In the interval – π , π all the values of sin | x | are positive as well as | cos x | Hence in – π , π , equation gets reduced to, 2 sin ⁡ x = 3 cos ⁡ x Taking log on both sides, sin ⁡ x log ⁡ 2 = cos ⁡ x log ⁡ 3 ⇒ tan ⁡ x = log ⁡ 3 / log ⁡ 2 , value of tan x are positive in 1 s t and 3 r d quadrant and negative in 2 n d and 4 t h quadrant but positive for tan ⁡ x in all the values of x in – π , π . Hence, tan x will repeat its value in all 4 quadrants, so the number of solutions are 4 .