if sinQ + cosQ = 1, prove that sin 2Q = 0 - Maths - Trigonometric Functions

Question

if sinQ + cosQ = 1, prove that sin 2Q = 0

Vipin Verma · Accepted Answer

sinQ + cosQ = 1
Squaring both sides we get
(sinQ + cosQ )2= 12
=> sin2Q+cos2Q+2sinQcosQ=1
=>1+2sinQcosQ=1 (since sin2Q+cos2Q=1)
=>2sinQcosQ=1-1
=>sin2Q=0 (since 2sinAcosA=sin2A)
Hence proved

if sinQ + cosQ = 1, prove that sin 2Q = 0.