trig functions

[jinx24]

Hi all! I am really having trouble with this type of question.

"Simplify the expression"

6 sec (A)/ (tan (A) + cot (A))

The only thing I can think of doing is to expand each term into sine or cosine.

6 (1/cos (A)) / ((sin/cos)(A) + (cos/sin)(A))

I am stuck at this point.

Thank you

 

[dagr8est]

(6/cosA)/([sin^2A+cos^2A]/sinAcosA)
=(6sinAcosA/cosA)/1
=6sinA

Haven't done trig in awhile but I think that's correct.

 

[soroban]

Hello, jinx24!

Simplify the expression: \(\displaystyle \,\frac{6\cdot\sec A}{\tan A\,+\,\cot A\)

The only thing I can think of doing is to expand each term into sine or cosine.

\(\displaystyle \L\;\;\;\frac{\frac{6}{\cos A}}{\frac{\sin A}{\cos A}\,+\,\frac{\cos A}{\sin A}}\;\;\) . . . good!

Multiply top and bottom by \(\displaystyle \sin A\cdot\cos A:\)

\(\displaystyle \L\;\;\frac{\sin A\cdot\cos A}{\sin A\cdot\cos A}\,\cdot\,\frac{\frac{6}{\cos A}} {\frac{\sin A}{\cos A}\,+\,\frac{\cos A}{\sin A}}\;=\;\frac{\6\cdot\sin A}{\sin^2A\,+\,\cos^2A}\;=\;\frac{6\cdot\sin A}{1}\;=\;6\cdot\sin A\)