Question

Show that (sin theta +cos theta)^2– (sin theta – cos theta )^2= 2 sin 2theta​​

Answer 1

Answer:

We have: (sin(θ)+cos(θ))2+(sin(θ)−cos(θ))2

Let’s begin by expanding the terms within the parentheses:

=sin2(θ)+2sin(θ)cos(θ)+cos2(θ)+sin2(θ)−2sin(θ)cos(θ)+cos2(θ)

=2sin2(θ)+2cos2(θ)

=2(sin2(θ)+cos2(θ))

=2(cos2(θ)+sin2(θ))

One of the Pythagorean identities is cos2(θ)+sin2(θ)=1 . We can use this in our proof to get:

=2×1

=2 (Q.E.D.)

Answer 2

Answer:

ʜᴏᴩᴇ ᴛʜɪꜱ ᴡɪʟʟ ʜᴇʟᴩ yᴏᴜ..