Question

Simplify: (sin θ − cos θ)2 − (sin θ + cos θ)2

a. -4sin(θ)cos(θ)
b. 2
c. sin^2θ
d. cos^2θ

Answer 1

Answer:

The  Solution is below. That is the option a. -4sin (θ)cos (θ)

Step-by-step explanation:

Simplify: (sin θ − cos θ)2 − (sin θ + cos θ)2

Solution:

We know the Identity

$A^{2}- B^{2}=(A+B)(A-B)$

Applying this Identity we get

$(\sin \theta - \cos \theta)^{2} -(\sin \theta + \cos \theta)^{2} =((\sin \theta - \cos \theta)+(\sin \theta + \cos \theta))((\sin \theta - \cos \theta)-(\sin \theta + \cos \theta))$

Now Plus sin θ Minus sin θ and Plus cos θ Minus cos θ will cancel each other then we have,

$(\sin \theta - \cos \theta)^{2} -(\sin \theta + \cos \theta)^{2} =(2\sin \theta)(-2\cos \theta)\\(\sin \theta - \cos \theta)^{2} -(\sin \theta + \cos \theta)^{2} =-4\sin \theta\cos \theta\\\\As\ Required\ in\ option\ a.$

The  Solution is the option a. -4sin (θ)cos (θ)