sgriffith354
Answered

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(sinx)(tanx+cotx)
I know it =secx but I don't know how to get to it​

Sagot :

sqdancefan

9514 1404 393

Explanation:

It is often useful to put everything in terms of sine and cosine.

  sin(x)·(tan(x) +cot(x))

  = sin(x)·(sin(x)/cos(x) + cos(x)/sin(x))

  = sin(x)²/cos(x) +cos(x) . . . . . . use the distributive property*

  = (sin(x)² +cos(x)²)/cos(x) . . . . . combine terms over a common denominator

  = 1/cos(x)

  = sec(x)

_____

* The expression inside parentheses could have been combined to ...

  (sin(x)² +cos(x)²)/(sin(x)·cos(x))

Then the sin/sin factors cancel, leaving the expression on line 4.

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