Question

show that (sin theta+cos theta)^2 -(sin theta - cos thetaa)^2= 2 sin theta​

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.)

Step-by-step explanation: