
Trigonometry

sin^{2}θ  
=  1 + cosθ  
1  cosθ 
EXAMPLE [1] Show that cos 2x = cos^{2}x  sin^{2}x
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
cos^{2}x  sin^{2}x  
=  1  tan x  
cos^{2}x + sin x cos x 
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
cos^{4}t  sin^{4}t  
=  cot^{2 }  
sin^{2}t 
EXAMPLE
Show that tanx = cosec2x  cot2x
Step by step working of example with video on separate page
Ratio Identities
sinθ  
tanθ =  
cosθ 
cosθ  
cotanθ =  
sinθ 
Reciprocal Identities
1  
secθ =  
cosθ 
1  
cosecθ =  
sinθ 
1  
cotanθ =  
tanθ 
Pythagorean Identities
sin^{2}θ + cos^{2}θ = 1
sec^{2}θ = 1 + tan^{2}θ
cosec^{2}θ = 1 + cot^{2}θ
sin^{2}θ is said as sine squared theta
NOTE sin^{2}θ 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.
