Introduction to proving Trig identities

Sorry for not being able to upload my video on Monday.
Now today's topic is Trig identities. Is you watch my video on topics you need to know in Calculus, the first topic i mentioned was Trig Identities.
Now lets start, trigonometry is study of sides and angles of a triangle.
We have three trig ratios namely:
Sine
Cosine
Tangent.

To remember them easily we use a mnemonic SOHCAHTOA
Sinx=opp/hyp
cosx=adj/hyp
tanx=opp/adj

Proving of Trig Identities.

Applying Pythagoras theorem,
x²+y²=r²
(rcosx)²+(rsinx)²=r²
r²cos²x+r²sin²x=r²
divide through by r² we have
sin²x+cos²x=1 (1st identity)
making sin²x subject of formula we have:
sin²x=1-cos²x (2nd identity)
Making cos²x subject of formula :
cos²x=1-sin²x.(3rd identity)
sin²x/cos²x=tan²x (4th identity)
cos²x/sin²x=cot²x.(5th identity)

inverse Identities

1/sin²x =cosecx
1/cos²x=sec²x
1/tan²x = cot²x.

Other Identities :

Sin²x+cos²x =1
dividing through by sin²x
sin²x/sin²x +cos²x/sin²x =1/sin²x.
1+cot²x=cosec²x.(6th identity)
sin²x +cos²x =1
dividing through by cos²x
sin²x/cos²x +cos²x/cos²x =1/cos²x.
tan²x+1=sec²x (7th identity).

I hope you understand the derivation of the seven identities.

Thanks for reading this blog post, you can check out my youtube video on this topic, I will endeavor by God's grace on Thursday I will release a post on more examples on Trig identities.

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