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Trigonometry
Identities

 

Strategy For Proving A Trigonometric Identity

[1] Usually start with the more complicated side
[2] Attempt to simplify this side to the less complicated side
[3] If you cannot see any obvious way to proceed
then express everything on the more complicated side
in terms of sin and cos
and then try to form the expression on the simpler side

 

Videos of examples of the approach to
"Show that ..." type of questions

 

Video 1 has 4 examples

EXAMPLE [1] Show that tanθ = sinθ/cosθ
EXAMPLE [2] Show that sin2θ + cos2θ = 1
EXAMPLE [3] Show that 1 + tan2θ = sec2θ
EXAMPLE [4] Show that

sin2θ  

=1 + cosθ
1 - cosθ  

 

Video 2 has 3 examples

EXAMPLE [1] Show that cos 2x = cos2x - sin2x
EXAMPLE [2] Show that sin(π/2 - x) = cos x
EXAMPLE [3] Show that cosec 2x = 0.5 sec x cosec x

 

Video 3 has 1 example

EXAMPLE Show that

cos2x - sin2x  

=1 - tan x
cos2x + sin x cos x  

 

Video 4 has 3 examples
The working for each example together with the video
is shown on separate pages
but the video is also show below

EXAMPLE [1] Show that cosθ tanθ = sinθ
Step by step working of Example 1 with video on separate page
EXAMPLE [2] Show that cos x (cosec x + tan x) = cot x + sin x
Step by step working of Example 2 with video on separate page
EXAMPLE [3] Show that

cos4t - sin4t  

=cot2
sin2t  

Step by step working of Example 3 with video on separate page

 

Video 5 has 1 example

 

Video 6 has 1 example
The working for this example together with the video
is shown on a separate page
but the video is also show below

EXAMPLE
Show that tanx = cosec2x - cot2x
Step by step working of example with video on separate page

 

 

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Ratio Identities

  sinθ
tanθ =
  cosθ

 cosθ
cotanθ =
  sinθ

Example Using Tan = Sin / Cos


Reciprocal Identities

  1
secθ =
  cosθ

  1
cosecθ =
  sinθ

 1
cotanθ =
  tanθ


Pythagorean Identities

sin2θ + cos2θ = 1

sec2θ = 1 + tan2θ

cosec2θ = 1 + cot2θ

sin2θ is said as sine squared theta
NOTE    sin2θ    means    (sinθ)2

Proof of Pythagorean Identities


EXTERNAL LINK
Table of Trig Identities [1]

EXTERNAL LINK
Table of Trig Identities [2]

EXTERNAL LINK
Table of Trig Identities [3]

EXTERNAL LINK
Table of Trig Identities [4]

EXTERNAL LINK
Table of Trig Identities [5]


EXTERNAL LINK
Proofs and Examples

EXTERNAL LINK
10 Worked Examples

Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.
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