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

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me prove this Trig identity: {{{ (tany+coty)sinycosy = 1 }}}      Log On


   



Question 295301: Please help me prove this Trig identity:
+%28tany%2Bcoty%29sinycosy+=+1+

Found 2 solutions by Edwin McCravy, CharlesG2:
Answer by Edwin McCravy(20060) About Me  (Show Source):
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me prove this Trig identity:
+%28tany%2Bcoty%29sinycosy+=+1+
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
+%28tany+%2B+coty%29sinycosy+=+1+
replacing tan and cot
+%28siny%2Fcosy+%2B+cosy%2Fsiny%29sinycosy+=+1+
distribute
+siny%2Fcosy+%2A+sinycosy+%2B+cosy%2Fsiny+%2A+sinycosy+=+1+
+siny+%2A+siny+%2B+cosy+%2A+cosy+=+1+
+sin%5E2%28y%29+%2B+cos%5E2%28y%29+=+1+
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
+1+=+1+
done