Combine these expressions into a single trig function or, if not possible, rewrite in terms of sin x and cos x:
1. (cos4x)(cosx)-(sin4x)(sinx)
2. sec^(4)x-tan^(4)x-2tan²x

Question

Combine these expressions into a single trig function or, if not possible, rewrite in terms of sin x and cos x:
1. (cos4x)(cosx)-(sin4x)(sinx)
2. sec^(4)x-tan^(4)x-2tan²x

anonymous · Answer

1st cos(5x)

anonymous · Answer

?

anonymous · Answer

cos(a+b)=cosacosb-sinasinb
put a=4x nd b=x

anonymous · Answer

2nd sin^2x+cos^2x

anonymous · Answer

Can you show your process?

turingtest · Answer

do you understand the first one?

turingtest · Answer

here's what I'm using http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

anonymous · Answer

Yea I got the first one now.

turingtest · Answer

so for the next we can do difference of squares on the first two terms

turingtest · Answer

$$\sec^4x-\tan^4x-2\tan^2x=(\sec^2x-\tan^2x)(\sec^2x+\tan^2x)-2\tan^2x$$

turingtest · Answer

how does this help us?
look at the first set of parentheses

anonymous · Answer

It equals 1?

turingtest · Answer

yup :)
so what do we have left?

anonymous · Answer

sec²x+tan²x-2tan²x

turingtest · Answer

...continue

anonymous · Answer

(1/cos²x)+(sin²x/cos²x)-(2sin²x/cos²x)
(1+sin²x-2sin²x) / cos²x

turingtest · Answer

you have over-complicated things...

turingtest · Answer

sec²x+tan²x-2tan²x=sec²x-tan²x

anonymous · Answer

Then that equals 1?

turingtest · Answer

looks like it, eh?
sorcery!

anonymous · Answer

sorry @enchantixPixie , i went to sleep since it was 4 in d morning here:)