Trigonometric proof project

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

how would i complete this problem two different ways?

Mar 26th, 2015

Where is the problem?

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Mar 26th, 2015


Mar 26th, 2015
trig_proof_problem.png

Ok, I'll work on this now.

Mar 26th, 2015

Here's one way:

(sint + cost)^2 = sin^2t + 2sintcost + cos^2t = 2sintcost + (sin^2t + cos^2t) = 2sintcost + 1

Then,

(2sintcost + 1) / sintcost = 2 + 1/sintcost = 2 + sectcsct


Now I'll work on another way

Mar 26th, 2015

(sint + cost)^2 / sintcost = (sint+cost)(sint+cost) / sintcost

= (1/cost + 1/sint)(sint + cost)

= (sect + csct)(1/csct + 1/sect)

= sect/csct + sect/sect + csct/csct + csct/sect

= sect/csct + 1 + 1 + csct/sect

= 2 + sec^2t/sectcsct + csc^2t/sectcsct

= 2 + (sec^2t + csc^2t) / sectcsct

= 2 + sectcsct / (cos^2t+sin^2t)

= 2 + sectcsct / 1

= 2 + sectcsct

Mar 26th, 2015

Thanks!

Mar 26th, 2015

You're welcome:)

Mar 26th, 2015

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