Jessica G.

asked • 04/28/15

Prove the identities vsecx- tanx/secx+tanx = 1/secx+tanx

help me 

Jon P.

tutor
The way you've written this is unclear.  There seem to be a lot of missing parentheses.  And does "v" mean square root?  If so, what exactly is it the square root of?  (Again, use parentheses.)
Report

04/28/15

Jessica G.

(squrtsecx- tanx/secx+tanx) = (1/secx+tanx)
Report

04/28/15

Stephanie M.

tutor
Hi Jessica,
 
Your formula is still very unclear. Right now, you've written:
 
√(secx) - tanx/secx + tanx = 1/secx + tanx
 
That means that only the secx is under the square root, that only the first tanx is in the numerator of the fraction on the left-hand side and that only the second secx is in the denominator of the fraction on the left-hand side, and that only the secx is in the denominator of the fraction on the right-hand side.
 
You'll need to surround the quantity under the square root sign with parentheses, surround the numerator of both fractions with parentheses, and surround the denominator of both fractions with parentheses.
 
For example, you might write:
 
(√(secx - tanx)) / (secx + tanx) = (1) / (secx + tanx)
 
which means:
 
(√(secx - tanx)) / (secx + tanx) = 1 / (secx + tanx)
Report

04/29/15

1 Expert Answer

By:

Stephanie M. answered • 04/29/15

Tutor
5.0 (890)

Private Tutor - English, Mathematics, and Study Skills
About this tutor ›
About this tutor ›
I think I figured out what you mean. You should write:
 
√((secx - tanx) / (secx + tanx)) = 1 / (secx + tanx)
 
This means:
 
√((secx - tanx) / (secx + tanx)) = 1 / (secx + tanx),
 
where everything on the left-hand side is under the square root sign.
 
 
Let's simplify that.
 
 
Square both sides to get rid of that square root sign:
 
(secx - tanx) / (secx + tanx) = 12 / (secx + tanx)2
 
 
Multiply both sides by (secx + tanx) to cancel out terms in both denominators:
 
secx - tanx = 1 / (secx + tanx)
 
 
Multiply both sides by (secx + tanx) again to cancel out the last term in the denominator:
 
(secx + tanx)(secx - tanx) = 1
 
 
Foil out the left-hand side and combine like terms:
 
sec2x - secxtanx + secxtanx - tan2x = 1
sec2x - tan2x = 1
 
 
Add tan2x to both sides:
 
sec2x = 1 + tan2x
 
 
That's one of your trig identities, 1 + tan2x = sec2x, so apply that to get...
 
sec2x = sec2x
 
 
You've proved the two sides are equal.
Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.