This post is part of a series of posts on Trigonometry. To see all the posts, click on the tag #TrigonometryTutorials below. This is the post you should read before you read this.
Here are a few trig identities that are very important to remember:
Identity 1:
sin2x+cos2x=1
Proof: Use the Definition of the trig functions: sinx=ho and cosha
(ho)2+(ha)2=1
h2o2+h2a2=1
Multiply both sides by h2
a2+o2=h2
This is just the Pythagorean Theorem! So this holds true. ■
A variation of Identity 1 can be achieved by:
dividing both sides by sin2x
1+cot2x=cscx
dividing both sides by cos2x
tan2x+1=secx
Identity 2: sinx=cos(90∘−x)
In a Right angled triangle, if one of the angles is x, The other angle will be 90−x (the angle other than the right angle, that is.). The opposite angle of one angle is the adjacent of the other angle, therefore sinx=cos(90∘−x).
Using the same reasoning, these other identities can be obtained:
cosx=sin(90−x)
secx=csc(90−x)
cscx=sec(90−x)
tanx=cot(90−x)
cotx=tan(90−x)
The Next post in this series is here
#CosinesGroup
#TrigonometryTutorials
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