How does my book go from this step to the next (trig)

[frasifrasi]

OK, in an example, we are given:

"T
(θ)= 2 cos^2 (θ) +sin^2 (θ) − sin (θ) + 3
=cos^2 (θ) − sin θ + 4.
Then Tθ
(θ)= −2 cos θ sin θ − cos θ =
−cos θ(
2 sinθ + 1)"

can anyone explain what happened from step 1 to 2--i am completely lost?

Thanks.

 

[NateTG]

OK, in an example, we are given:

"T
(θ)= 2 cos^2 (θ) +sin^2 (θ) − sin (θ) + 3
=cos^2 (θ) − sin θ + 4.
Then Tθ
(θ)= −2 cos θ sin θ − cos θ =
−cos θ(
2 sinθ + 1)"

can anyone explain what happened from step 1 to 2--i am completely lost?

$$\sin^2 \theta + \cos^2 \theta = 1$$
so
$$\sin^2 \theta = 1 - \cos^2 \theta$$
Now, substitute in for step 1 and simplify.

 

[frasifrasi]

Geez, I am embarassed.