Question

Thanks in advance

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

−sin2 Θ
−cos2 Θ
0
−2sin(Θ)cos(Θ) − cos(Θ) + sin(Θ) − 1

Answer 1

(sin O - cos O) - (sin O + cos O)^2
= sin O - cos O - (sin^2 O + cos^2 O + 2 sin O cos O)
= sin O - cos O - ( 1 + 2 sin O cos O)
Distributing the negative over the second set of parentheses:-
= sin O - cos O - 1 - 2 sin O cos O
= -2 sin O cos O - cos O + sin O - 1 (answer)

Its the last choice.

Answer 2

−2sin(Θ)cos(Θ) − cos(Θ) + sin(Θ) − 1

Explanation:

`(sin O - cos O) - (sin O + cos O)^2`

`(sin A + cos A)^2= sin^2A + cos^2A+2sinAcosA`

Apply identity, sin^2A+cos^2A= 1

`(sin O - cos O) - (sin O + cos O)^2`

Replace 1 for sin^2O+cos^2O= 1

`(sin O - cos O) - (sin O + cos O)^2`

`(sin O - cos O) -(1+2sin(O)cos(O))`

REmove the parenthesis and simplify if possible

`sin O - cos O -1-2sin(O)cos(O))`

So option D is correct