Trigonometry Problem!

[virtualmaster999]

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Hey everyone!

Kinda got stuck on number 146 from the regular destroyer. I looked at the solution but still cant get it. Can someone give me some other way to solve this maybe, or a further breakdown of the problem?

Thanks!!

 

[Lnguyen7]

Would be great if you could post the problem or picture it. Many can help you right away, but they don't have the book or the version that you are talking about.

 

[virtualmaster999]

Yeah it's (Tanx +Cotx)/(cscx)

It's supposed to come out to secant x somehow

 

[DAT Destroyer]

Hey everyone!

Kinda got stuck on number 146 from the regular destroyer. I looked at the solution but still cant get it. Can someone give me some other way to solve this maybe, or a further breakdown of the problem?

Thanks!!

(tan x + cot x)/csc x.
Write everything in terms of sine and cosine.
You should know the following:
tan x = sin x / cos x . cot x = cos x/ sin x and csc x = 1/sin x
If you work the top of the fraction you should get : ( sin^2(x)+cos^2(x))/(sin x cos x) = 1/(sin x cos x)
And finally you divide by csc x which is the same as multiplying by sin x you get:
Sin x/ sin x cos x = 1/cos x = sec x.

 

[virtualmaster999]

(tan x + cot x)/csc x.
Write everything in terms of sine and cosine.
You should know the following:
tan x = sin x / cos x . cot x = cos x/ sin x and csc x = 1/sin x
If you work the top of the fraction you should get : ( sin^2(x)+cos^2(x))/(sin x cos x) = 1/(sin x cos x)
And finally you divide by csc x which is the same as multiplying by sin x you get:
Sin x/ sin x cos x = 1/cos x = sec x.

Finally understand it! Thanks so much!