What is the value of 1-sin2x?
Find the value of 1-sin2x.
Apply the trigonometric identities:
sin2x+cos2x=1⋯1sin2x=2sinxcosx⋯2
Substitute the value of 1 from equation 1 and the value of sin2x from the equation 2 into the given equation:
1-sin2x=sin2x+cos2x-2sinxcosx...(3)
Apply the algebraic identity a-b2=a2+b2-2ab in the equation 3:
1-sin2x=sinx-cosx2
Hence, the value is 1-sin2x=sinx-cosx2.