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Sir, explain vividly to me #TRIGONOMETRIC_IDENTITIES and how to applied them. it sound like a greek to me whenever i come-across any ? That says: ''prove tanx, cotx,sin°,cos^2° e.t.c"

for example,
prove that 1+tanx/1+cotx=tanx.
In my texbook, the author solve it by using "LHS" and "RHS throughout. But i don't understand!!!

Hi Fran,
First of all, LHS and RHS refer to the left and right hand sides of the equation respectively, if you didn't already know.
Now, to be successful with these kind of problems you need to know the basic identities including;
tanx = sinx/cosx
cos▓x + sin▓x = 1
secx = 1/cosx
cosecx = 1/sinx
cotx = 1/tanx
These are the ones that get manipulated mostly and it's not so difficult to spot them with some practice.

To the example, it is best to start by simplifying the denominator on the LHS;
1 + cotx = 1 + (1/tanx)
= (tanx + 1)/tanx

At this point there are two ways to go about the proof. You could resolve the LHS on its own and show that it is equal to the RHS, or you could combine the two sides and show that the equation is still consistent.

Method 1:
(1 + tanx) / (1 + cotx) = (1 + tanx) / [(tanx + 1)/tanx]
= (1 + tanx) . tanx/(tanx + 1)
= tanx
Hence, the proof.

Method 2:
From (1 + tanx) / (1 + cotx) = tanx, we have
1 + tanx = tanx(1 + cotx)
1 + tanx = tanx [(tanx + 1)/tanx]
1 + tanx = tanx + 1
And again we have the proof by showing consistency.

I hope it is clear.



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Ahmed Salami


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