The value of x in 0,π2 satisfying the equation sinxcosx=14 is
π6
π3
π8
π4
π12
Explanation for the correct option:
Find the required value:
Given: sinxcosx=14
Multiplying by 2 on both sides, we get
⇒2sinxcosx=24⇒sin2x=12[∵2sinθcosθ=sin2θ]⇒2x=sin-112⇒2x=sin-1sinπ6[∵sinπ6=12]⇒2x=π6⇒x=π12
Hence, option (E) is the correct answer.