find the equation of tangent to the curve y= 2sinx +sin2x at x= pi/3 - Maths - Application of Derivatives

Question

find the equation of tangent to the curve y= 2sinx +sin2x at x=
pi/3

Anuradha Sharma · Accepted Answer

y = 2sinx+sin2xdydx=2cosx+2cos2xNow dydx at x = π3 is , =2cosπ3+2cos2π3=1-1=0So slope of tangent m = 0 So at x = π3, y =  2sinπ3+sin2π3=332So tangent at 332,π3 with slope m = 0 is    y -π3= mx-332⇒y -π3 = 0So, y = π3