Using Double-Angle Identities to Verify Other Trig Identities (MathAngel369)

Verifying Trig Identities Using the Double-Angle trig identities (MathAngel369)

In this discussion, we are going to verify trigonometric identities using the double-angle identities.

Here is an outline of this discussion:
(Skip ahead if you like)

Verify that (1-cos2x)/sin2x = tanx
(Skip to 0:16)

Verify that sin2x = 2tanx/(1+ tan^2x)
(Skip to 3:08)

Let’s begin!

Verify that (1-cos2x)/sin2x

We begin with the left-hand side of the equation and slowly manipulate it until it looks like the right-hand side.

LHS
= (1-cos2x)/sin2x
= (1-(1-2sin^2x)) / 2sinxcosx
= (1-1+2sin^2x) / 2sinxcosx
= 2sin^2x / 2sinxcosx
= sinx / cosx
= tanx
= RHS

Verify that sin2x = 2tanx/(1+ tan^2x)

This time, let us begin with the right-hand side and slowly manipulate it until it looks like the left-hand side.

RHS
= 2tanx/(1+ tan^2x)
= (2sinx / cosx )/ (sec^2x)
= (2sinx / cosx )/ (1 / cos^2x)
= 2sinxcos^2x / cosx
= 2sinxcosx
= sin2x
= LHS

We are done!

I hope that I can assist you in your math journey!

Sincerely,

➕MathAngel369➕

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