How Do You Solve Trig Identities Using Basic Trigonometric Equations?

[SirMarksAlot]

Homework Statement

(1 + cosθ) / (1 - cosθ) = (1 + secθ) / (secθ - 1)

Homework Equations

using only the quotient identities, pythagorean identities, and reciprocal identities

The Attempt at a Solution

didnt know where to start...

 

[Mark44]

Start on the right side.

 

[Mentallic]

lol Mark44.

Key word is reciprocal identity, and this should be obvious since [itex]cos\theta[/itex] is the reciprocal of [itex]sec\theta[/itex] and vice versa.

 

[SirMarksAlot]

kk got it.

RS
=(1 + secθ) / (secθ - 1)
=(1 + 1/cosθ) / (1/cosθ - 1)
=([cosθ+1] / cosθ) / ([1-cosθ] / cosθ)
=[(cosθ+1)(cosθ)] / [(1-cosθ)(cosθ)]
cancel cosθ
=(1 + cosθ) / (1 - cosθ)

 

[SirMarksAlot]

oh wow, all these question are so easy now, thanks for the advice about the reciprocal.

 

[Mentallic]

No problem

I remember starting off with trig identities... I would have to say that was the hardest and most stressful topic to learn. If you don't have someone like your teacher to help you out with those, you can get lost in a question for hours! Well, at least that's what me and a few of my friends did.

It all comes to you eventually with much practice on this topic though. Good luck.