Which of the following are identities? Check all that apply.

Question

(Points : 2)
sin2x = 1 - cos2x

sin2x - cos2x = 1

tan2x = 1 + sec2x

cot2x = csc2x - 1

Question 4. 4. Which of the following equations are identities? Check all that apply.
(Points : 2)








Question 5. 5. The expression sinx(cscx - cotx cosx) can be simplified to _____.
(Points : 2)
sin2x

sin2x - cscx

cos2x

sinx - tanx

Question 6. 6. The expression (secx + tanx)2 is the same as _____.
(Points : 2)
sec2x + tan2x

sec2x + 2cscx + tan2x

1 + 2cscx

1 + 2tan2x + 2secx tanx

Question 7. 7. Which of the following would be an acceptable first step in simplifying the expression ?
(Points : 2)




tanx + sinx

Question 8. 8. All identities are equations, and all equations are identities.
(Points : 2)
True

False

Question 9. 9. Which of the following is an identity?
(Points : 2)
sin2x - cos2x = 1

csc2x + cot2x = 1

(cscx + cotx)2 = 1

sin2x sec2x + 1 = cot2x csc2x

Question 10. 10. Which of the following is not an identity?
(Points : 2)
cos2x cscx - cscx = -sinx

sinx(cotx + tanx) = secx

cos2x - sin2x = 1- 2sin2x

csc2x + sec2x = 1

Answer 1

Hey, there is a limit !
I will do the first one, then you try the rest.

Which of the following are identities? Check all that apply.
(Points : 2)
sin2x = 1 - cos2x
I assume you mean sin^2 x not sin 2x
This is the same as
sin^2 x + cos^2 x = 1
which IS an identity.

sin^2x - cos^2x = 1 No way

tan2x = 1 + sec2x
sin^2 x/cos^2x = 1 + 1/cos^2 x
is
sin^2 x cos^2 x = 1 which is the same No way

cot2x = csc2x - 1
is
cos^2 x/sin^2 x = 1/sin^2 x -1
cos^2 x = 1 - sin^2 x
cos^2 x + sin^2 x = 1 YES