3. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
Lets make a list of the identities we can
use, so we can see thing in a clearer view.
Reciprocal Identities
1
cscx = sinx
sinx tanx =
cosx
1
secx =
cosx
cosx
1 cotx =
cotx = sinx
tanx
4. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
Lets make a list of the identities we can
use, so we can see thing in a clearer view.
Reciprocal Identities Special Trigonometric Identities
1 2 2
cscx = sinx cos + sin = 1
sinx tanx =
cosx 2
= csc
2
1 + cot
1
secx = 2
cosx 1 + tan = sec 2
1 cotx = cosx
cotx = sinx
tanx
5. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
DO NOT CROSS
Drop in a wall and DO NOT CROSS IT!
Now lets solve this baby to see if
Moon Light Knight is Tuxedo Mask.
DO NOT CROSS
6. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
Remember that
reciprocal identity? 2
tan x + 1
sinx
tanx = cosx 2
csc x 1
We can sub it in.
DO NOT CROSS
DO NOT CROSS
7. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
2
tan x + 1
2
csc x 1
Remember the special Reduces
2
( sec x 1 ) + 1
trig identities. With a
little rearranging we 2
DO NOT CROSS
cot x
can sub them in.
2
tan = sec 2 1
2 2
cot = csc 1
DO NOT CROSS
8. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
2
tan x + 1
2
csc x 1
Reduces
2
( sec x 1 ) + 1
2
DO NOT CROSS
cot x
2
sec x
This is what it looks
like cleaned up. 2
cot x
DO NOT CROSS
9. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
2
tan x + 1
2
csc x 1
Reduces
2
( sec x 1 ) + 1
2
DO NOT CROSS
cot x
2
sec x
2
cot x
1
Took the reciprocal to get sec x
it out of the denominator.
2
( cot x )
2 DO NOT CROSS
10. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
2
tan x + 1
2
csc x 1
Reduces
2
( sec x 1 ) + 1
2
DO NOT CROSS
cot x
2
sec x
2
cot x
1
Remember that
2
sec x ( cot x )
2 DO NOT CROSS
reciprocal identity, Do 2
2
sec x tan x
a little rearranging and
we can subbed it in.
1
tanx = cotx
11. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2 Remember that
reciprocal identity.
DO NOT CROSS
2 2 We can sub it in.
2 sec x tan x
tan x + 1 sinx
tanx =
2 cosx
csc x 1
Reduces
2
( sec x 1 ) + 1
2
DO NOT CROSS
cot x
2
sec x
2
cot x
1
2
sec x ( cot x )
2 DO NOT CROSS
2 2
sec x tan x
12. Prove that the Moon Light Knight is Tuxedo Mask.
Moon Light Knights Tuxedo Masks
Equation is: 2
sin x Equation is: 2
+1 sin x
cos x
2
2
= 2
sec x
cos x
2
csc x 1
Moon Light Knight Tuxedo Mask
2
sin x
+1
cos x
2 2
sin x
2
csc x 1
= 2
sec x
cos x
2
DO NOT CROSS
2 2
2 sec x tan x
tan x + 1
2
csc x 1
Reduces
2
( sec x 1 ) + 1
2
DO NOT CROSS
cot x
2
sec x
2
sec x
2
cot x
1
( cot x )
2 DO NOT CROSS
Q.E.D
2 2
sec x tan x