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