Trig identities?

Question

Form an identity by completing the following equation.
4cos^2 t + 3sin^2 t =

Thanks for the help!

Here are the choices...
a. cos2 t + 3
b. cos t + 1
c. 3cos2 t + 1
d. None of the above.

Here are the choices...
a. cos^2 t + 3
b. cos t + 1
c. 3cos^2 t + 1
d. None of the above.

Answer 1

4 cos ² t + 3 (1 - cos ² t)
cos ² t + 3
OPTION a)

Answer 2

Knowing that

cos^2(t) +sin^2(t) =1
4cos^2 t + 3sin^2 t can be written as

3(cos^2(t) + sin^2(t)) +cos^2(t)=
3(1) +cos^2(t) =
3 +cos^2(t)

Answer 3

The key identity: cos^2t + sin^2t = 1, cos^2t = 1 - sin^2t

4cos^2 t + 3sin^2 t = 4(1 - sin^2t) + 3sin^2 t
= 4 - sin^2t

Answer 4

4cos^2(t) + 3sin^2(t)
=cos^2(t)+3cos^2(t)+3sin^2(t)
=cos^2(t)+3(cos^2(t)+sin^2(t))
=cos^2(t)+3

Answer 5

Use cos^2t + sin^2t = 1, so

cos^2t + cos^2t + cos^2t + cos^ t + sin^2t + sin^2t + sin^2t

= cos^2t + 3

hope this helps, Twiggy

Answer 6

D) None