The number of solutions, the equation s i n 4 x + c o s 4 x = s i n x c o s x has, in [ π , 5 π ] is/are

Step-by-step solution

s i n 4 x + c o s 4 x = s i n x c o s x ⇒ ( s i n 2 x + c o s 2 x ) 2 - 2 s i n 2 x c o s 2 x = s i n x c o s x ⇒ 2 s i n 2 x c o s 2 x + s i n x c o s x - 1 = 0 ⇒ 2 s i n x c o s x - 1 s i n x c o s x + 1 = 0 ⇒ s i n 2 x = 1 …(i) x ∈ π , 5 π ⇒ 2 x ∈ 2 π , 10 π from (i), 2 x = 5 π 2 , 9 π 2 , 13 π 2 , 17 π 2 ⇒ x = 5 π 4 , 9 π 4 , 13 π 4 , 17 π 4 ⇒ The number of solutions = 4