The number of distinct solutions of the equation, log 1 2 ⁡ sin ⁡ x = 2 - log 1 2 ⁡ cos ⁡ x in the interval 0 , 2 π , is ________

Step-by-step solution

log 1 / 2 ⁡ sin ⁡ x = 2 - log 1 / 2 ⁡ cos ⁡ x l o g 1 / 2 sin ⁡ x cos ⁡ x = 2 sin ⁡ x cos ⁡ x = 1 4 sin ⁡ 2 x = ± 1 2 Number of solution = 8 .