# Trig worksheet 1

```Trig
Prove each identity;
.
1 . secx - tanx SInX -
1
secx
Identities
worksheet 3.4
name:
-
2.
1 + cos x = esc x + cot x
sinx
sin' 8
4.
-----=
3.
sec8sin8
tan8+ cot8
5.
., y = 12&quot;
cos ' Y - sin
- Sin Y
6.
csc 2 etan 2 e -1 = tan 2 e
7.
sec 2 e
sec e -1
8.
tan 2 x sin' x = tan' x - sin' x
-2 -
csc
2
e
sec8
cos8
tan8
cot8
1
Tria
Identities
name:
worksheet 3.4
Prove each identity:
1.
secx-tonxslnx= - sec X
2.
1&middot;,&middot; eosx
sinx
3.
seellsinll
tane + cote
4.
- -- - -
5.
., Y= 1- 2Sin
&middot;' Y
cos , y - Sin
6.
ese'Otan' II -1 = tan' II
7.
sec'O
esc' 0
sec' 11 - 1
8.
tan' x sin' x = tan' x - sin' x
.
--
1
sin'lI
seeO
cosO
esex + cot x
tanll_
1
cotO
Tris,
Identities
worksheet 3.4
rumle:
Prove each identity:
1
.
secx- t anxsrnx=-sec x
1.
_ ,_
\$1,,1)(.5&quot;.1'\'&quot;
&laquo;70 f\(
(.&lt;I):' ')(
'i!&gt; 1&lt;:\ 'Y
-..
lbS- '~
.
0l:S ~
....
sec8sin8
tan8+ cot8
....l-
eSC
J-.
. 2
srn 8
4.
-.-~
Co.
C
~c.9
..f.,..&quot; C9
s 1..-t c. &quot;l...
•
t;1 .....
5
of- '-&lt;0
2
':
. 2
~
=1
t. e
&quot;-
CoS
_'f • '&quot; r
\$I&quot;
c..d'S:
::0
0/5'
6.
6~oe&middot;~1.~) ,-t 1=
-\-p- L.(9--
8.
of-
-+- f - \ = (
eSc, ~
e- '&quot;
__
V
..
~
tan 2x sin2x = tan 2x - sin2 x
\
'is
l ,,&quot;-)(' )
J.- . CI
.,.
1
- I.
'2- ~
').
5(:.' (.,.. • \$'&quot; I)&lt;
~&quot;e
~
~ ~/
~ 16).
(gfc.7..~ _
sec. 't.(9 ,..
,~
J
, C~~ - 1=tan2.8
01\ ~-y
-::r
r-
-,....
_
1. Ai
&quot;
-
-
S'M &quot;I. ')(
tos.~ ftC
\V
./
/
V
c..~ '(9
&lt;;.A..,)
-= .,/'V
sec 2e
2
sec2 e _ 1 = csc 8
-;:;''f)
L.qs~
~ I ' &quot; t.-
~Z-8
[p; - ~ .
-:0
'-e-- -
~~
.
I ... .~.,...
~
:-.;;r:
I~C;:;. &quot; ~&laquo;9
()
&middot; lb~
. 2
. I =-J.-Sr&quot;&quot; l.'t&quot;
7.
v'
cot8
Cos t&quot;'@
-f.-..-fSl
X:SIn Y_=1~2sm ~
/_ &quot;&quot;'&quot;, ~ .... \$11'\ ~ - )
. . cos
\cg_~8
Sivt
_+--(;7
'c;&quot;
/~c~~ tan8
.
.... &laquo;rte
~9-
cot- &yen;
+-
f)('
if
5, .... 19
~e-
c-
J
Y.I
&quot; •..,'&gt;It
_
(6;&gt;15
5:5
~&quot;~I\&pound; ~ ~
....
1-
-
~(
I
S iI\I\&lt;&quot;
2
Co.S?(
3.
1 + cas x = esc x + cot x
sinx
-
::
II
2.
~ 'l-,y -911 '2 'X -;.
Tri;z
Identities
9. _ (sine 'I. ~s~r+J:'ln~-coser = 2
~rt.G_f-~fo?oS~
,....--,------ ..-:--;:: '. ... ' {L.
worksheet 3.4
::::=&quot;\
(Sine + cose)( tane+ cote) = sec 8 + csce
10.
==
..
.' ......
s;.. g -1--(9 ...
,,* C) t-(.Q!) &amp;;....J: &amp;
;;
~
~
+ co!&gt; ~ ,ot;&lt;S&gt;
::
5&quot; t., &amp;-
..
'S~&quot;~?-:: ~+-(~r ~ &gt;
f-
.-
(~
{
:::-
2-
-;.-r
~
~I '&quot;
1
\
eJ
C&gt; of (...OS
i
~ ~
-t ( &gt;I '&quot; (9 ... COS 0 )
~ QS ~ (
I
r,tI 'ell- ~~ of
j,.-V
IS 1\
51&quot;
7'
11. tan8-1
tone + 1
, SI&quot;,19
l-cot8
1 ... cot 8
1- tan- x = 1- 2 sin2 x
12. 1+ tan2x
(_~
~(5)-=
_
L6-;; (9
LOr&quot; 9
&lt;51'&quot; c9
(.o~ ()
'L&quot;,
S&quot;e to
+~(!7
5&quot;~c '-I'&quot;
+--..
((~.
.
5-e.:.
t-- .,
.le. -
\!:!! j
L
~
~ ~ J~
.
L
(~'&gt;.c9
-;; ,
V
f1
t.
'V'
&gt;&lt;
.
(
(07
csc x
1 - cos x
- .
l&gt;Cy(
-?
(~'2-. &lt;;I&quot;'~&quot;K&quot;
.
14. csc x - cot x = csc x + cot 2 x
4
4
2
~
_
v &middot;
_&lt;:/A.'N _c;.t&quot;,'1 &quot;, -1&lt;
13. coS x + 1
sin 3 x
'L~ &quot;'-&lt;&quot;05 1 &lt;1&lt;
c&lt;;;c IP ~ ~c. ~
&quot;
').?
-
c€ic9-'Qf'l~)( uc -''1('. c~f 1.&quot;1&lt;')
/,
,_ L
e-- /&quot;
=
~ _ &cent;'-----H--\
~I+-~O1. --v-l
-::.
-;&quot;', ~ (f (;~-l
L--
LeSe 2-'&laquo; ~ (01:: tty)
.
5,,,y(I-(orx )ll&quot;'c~
: :. . J \/
{
~(/&quot; /Yl /-
(Os
')C') -=- 5{~)&quot;
1-
(S't..y _
tan8 cot8
.
Gu......~iny + tany =siny
15. - - + - - = Sln8+cos8
esc,&gt;&quot;, 16. 1 + secy
see8 ese8
~
~
.
R.
y~'J
5,
V\
~I~
e-..j. &amp;lr\$-
, - tur
51(\
s ..&quot; ~
'1 +- CO!. :1
---------'~
\
&gt;
l+
I
\
{.OJ.'O&quot;
&lt;51&quot;&lt; (~ ... ~I-&quot;-
&pound;;A
(os. .,. I
~
&quot;.(,0&quot; oj )
(5+(~/
&quot;;1
(I
j
~
Trig Identity Quiz
Name
Prove the following identity
1) 2 cos etan ecsc
2)6cos
e= 2
cote
- I- - { cos e esc e
J = 6sm.
l
e
cot l e
,
,
3) 7 - -- sec e= 7 tan ecos ecsc e
esc e
```