Algebra/math

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Expert: - 9/6/2009


Question
sin(2A)=2sinA cosA
 =(2sinA cos^2A)/cosA
 =2tanA/sec^2A
 =2tanA/1+tan^2A

please explain it  

Answer
Hello Pratap,

To answer your question we will need a few trigonometric identities; I'll tell you which as we go along. Let's begin by giving a number to every step:

sin(2A)=2sinA cosA             ...(1)
=(2sinA cos^2A)/cosA           ...(2)
=2tanA/sec^2A                  ...(3)
=2tanA/1+tan^2A                ...(4)

You'll get step (1) by using:

sin(A+B)=sin(A)cos(B)+sin(B)cos(A),

and then making B=A.

For step (2) you are dividing and multiplying everything by cos(A).

From now on, just to make the notation a bit less ambiguous I'm going to write (cosA)^2 instead of cos^2A, OK?

In step (3), you are doing two things:

First, you are writing (sinA/cosA) as tanA.

Then you are writing (cosA)^2=1/(secA)^2

Finally in step (4) you are using the identity:

(secA)^2 = 1 + (tan)^2

That's it!

Hope this helps, let me know if you still have questions.
David  

Algebra

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