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

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

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

EXAMPLE Show that

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

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

Ratio Identities

Example Using Tan = Sin / Cos

Reciprocal Identities

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