Trigonometric Identities PAGE 1: The ones you MUST know! The expressions on this page are essential to know in the exam. Trig Exact Value Facts You must know all of these for substituting into expressions. Luckily though, your calculator will help check these in an exam if you are unsure… To help you learn them, try thinking of the graphs of sin and cos (i.e. when the cut the x- axis, and where they have maxima and minima. 3 2 2 2 3 2 1 cos(0) cos(2 ) 0 sin(0) sin( ) sin(2 ) 1 cos( ) 0 cos( ) cos( ) 1 sin( ) 1 sin( ) p p p p p p p p = = = = = -= = = = -= sin( ) sin( ) cos( ) cos( ) tan( ) tan( ) q q q q q q - =- - =+ - =- Identities that you MUST learn and know (Learn them now if you don‛t know them already!) 2 2 cos sin 1 A A + = 2 1 2 2 1 2 cos (1 cos2 ) sin (1 cos2 ) x x x x = + = - sin tan cos A A A = sin( ) sin cos cos sin cos( ) cos cos sin sin tan tan tan( ) 1 tan tan sin(2 ) 2sin cos 2 2 cos(2 ) cos sin A B A B A B AB A B A B A B A B A B A A A A A A – = – – = – – = = = - m m Remember that A and B can be ANY expression at all So, for example 2 2 sin (2 1) cos (2 1) x x + + + would still be 1. www.ssc-cgl2014.in For more free Video / Audio Tutorials & Study Material visit - www.ssc-cgl2014.in And for regular updates on our website like us on facebook - www.facebook.com/cgl.ssc2014 www.ssc-cgl2014.in
The expressions on this page are essential to know in the
exam.
Trig Exact Value Facts You must know all of these for
substituting into expressions. Luckily though, your calculator will
help check these in an exam if you are unsure To help you learn
them, try thinking of the graphs of sin and cos (i.e. when the cut
the x- axis, and where they have maxima and minima.
32 2
2
32
1 cos(0) cos(2 )
0 sin(0) sin( ) sin(2 )
1 cos( )
0 cos( ) cos( )
1 sin( )
1 sin( )
p p
p
p
p p p
p
= = = = =
- = = = =
- =
sin( ) sin( )
cos( ) cos( )
tan( ) tan( )
q q q q q q
- = - - = + - = -
Identities that you MUST learn and know (Learn them now if you
dont know them already!)
2 2cos sin 1A A + =2 1
2
2 12
cos (1 cos2 )
sin (1 cos2 )
x x
x x
= +
= -
sintan
cos
AA
A =
sin( ) sin cos cos sin
cos( ) cos cos sin sin
tan tantan( )
1 tan tan
sin(2 ) 2sin cos
2 2cos(2 ) cos sin
A B A B A B
A B A B A B
A BA B
A B
A A A
A A A
= =
=
=
= -
m
m
Remember that A and B can be ANY expression at all So, for
example 2 2sin (2 1) cos (2 1)x x + + + would still be 1.
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Trigonometric Identities
PAGE 2: Useful facts, but not essential to learn
You ought to be able to survive in the exam without knowing
these ones off by heart,
BUT
You should be able to derive them all if needed using the
equations on Page One [there have been past exam questions asking
you to do just this] MAKE SURE YOU KNOW HOW YOU CAN GET (OR CHECK)
EACH OF
THEM IF YOU NEED TO
Identities
2 21 tan secA A + =
2 2cot 1 cosA ec A + =
2
2
cos(2 ) 2cos 1
cos(2 ) 1 sin
A A
A A
= -
= -
2
2 tantan(2 )
1 tan
AA
A =
-
1 2sin(cos ) 1x x - = - (ones like this come up a lot in
differentiation.
You must know how to get it, it is not enough just to learn
it)
Exact Values
Technically you should know these already from Higher! I am not
sure whether they could come up in the exam Maybe better safe than
sorry
14 4 2
16 3 2
33 6 2
sin( ) cos( )
sin( ) cos( )
sin( ) cos( )
p p
p p
p p
= = = = = =
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cgl20
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on
