Question

solve |sinx+cosx|= |sinx|+|cosx| x € 0, 2π​

Answer 1

Answer:

Given ∣sinx+cosx∣=∣sinx∣+∣cosx∣

For 0≤x≤π/2

sinx+cosx=sinx+cosx

⇒0⩽x⩽π/2

For π/2⩽x⩽π,sinx>0cosx<0

LHS sinx−cosx>0x<3π/4

sinx−cosx<0x>3π/2

RHS : sinx+cosx

L.H.S



= RHS

For π⩽x<3π/2

LHS = ∣−sinx−cosx∣

RHS = ∣−sinx∣+∣−cosx∣

LHS = RHS ⇒π⩽x⩽3π/2

For 3π/2<x<2π

LHS :∣−sinx+cosx∣=∣cosx−sinx∣

RHS : ∣sinx∣+∣cosx∣

LHS



= RHS

⇒0⩽x⩽π/2 and π⩽x⩽3π/2

solution