SOLUTION: Please help me prove this Trig identity: {{{ (tany+coty)sinycosy = 1 }}}

Question 295301: Please help me prove this Trig identity:

Found 2 solutions by Edwin McCravy, CharlesG2:
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

`
Edwin
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Please help me prove this Trig identity:

define opp = opposite side, adj = adjacent side, hyp = hypotenuse
and hypotenuse is side opposite to the right angle in a right triangle
and sohcahtoa --> sin = opp/hyp, cos = adj/hyp, tan = opp/adj
and sin/cos = opp/hyp * hyp/adj = opp/adj = tan
and cos/sin = adj/hyp * hyp/opp = adj/opp = 1/tan = cot

replacing tan and cot

distribute

if circle has radius 1:
triangle 30-60-90 with 30 degree angle at center of circle, and hypotenuse being the radius:
sin 30 = opp/hyp = opp/1 = opp
cos 30 = adj/hyp = adj/1 = adj
Pythagorean Theorem --> opp^2 + adj^2 = hyp^2 --> sin^2 + cos^2 = 1

done

RELATED QUESTIONS
Please help me prove this Trig identity: {{{ cosxsecx/tanx = cotx... (answered by Fombitz)
please help me prove this identity:... (answered by Alan3354)
I need help with this trig identity. Prove the identity: cos^2x = 1-cos^2xtan^2 Please (answered by DrBeeee)
this is trig identities, if you could please help me prove the following identity true (answered by Fombitz)
Hi. How do I prove this equation to be an identity? (tanY + sec^2 Y - tan^2Y)/secY =... (answered by jim_thompson5910)
Hi, I am having trouble with my homework. I hope someone helps me with this. Prove... (answered by lwsshak3)
Please help. How can I prove the identity? Is there any online calculator for trig... (answered by Edwin McCravy)
how do i prove this trig identity?... (answered by stanbon)
Please help me with the following question. Prove this identity:... (answered by Alan3354,josgarithmetic,MathTherapy)