cos x + sin x tan x

midnightdreary · **Joined:** Mon, 9 Apr 2012 03:22:52 UTC **Posts:** 1

For some reason I am having real difficulty simplifying cos x + sin x tan x. Please assist.

Shadow · **Posted:** Mon, 9 Apr 2012 03:28:32 UTC

midnightdreary wrote:

For some reason I am having real difficulty simplifying cos x + sin x tan x. Please assist.

Factor out cos x.

Soroban · **Posted:** Mon, 9 Apr 2012 05:49:07 UTC

Hello, midnightdreary!

Quote:

$\text{Simplify: }\:\cos x + \sin x \tan x$

$$\cos x + \sin x\tan x \;=\;\cos x + \sin x\left(\frac{\sin x}{\cos x}\right)$

. . . . . . . . . . . . . . . $$=\;\cos x + \frac{\sin^2\!x}{\cos x}$

. . . . . . . . . . . . . . . $$=\;\frac{\overbrace{\cos^2\!x + \sin^2\!x}^{\text{This is 1}}}{\cos x}$

. . . . . . . . . . . . . . . $$=\;\frac{1}{\cos x}$

. . . . . . . . . . . . . . . $=\;\sec x$

emma157 · **Joined:** Sun, 8 Apr 2012 10:51:59 UTC **Posts:** 2

what if it was cot x instead of tan x.

Shadow · **Posted:** Wed, 11 Apr 2012 14:19:04 UTC

emma157 wrote:

what if it was cot x instead of tan x.

Then it's even easier. Write out what cotangent is, you should be able to do this immediately.

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cos x + sin x tan x

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