SOLUTION: if Tan A= √2-1 , prove that sin A.cosA =√2 /4

Algebra ->  Trigonometry-basics -> SOLUTION: if Tan A= √2-1 , prove that sin A.cosA =√2 /4      Log On


   

Question 695901: if Tan A= √2-1 , prove that sin A.cosA =√2 /4
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the following right angled triangle

Then for this triangle +tan+A+=+opp%2Fadj+=+%28sqrt%282%29-1%29%2F1+=+sqrt%282%29-1+,
By Pythagoras +hyp%5E2+=+opp%5E2+%2B+adj%5E2+ so
+hyp%5E2=%28sqrt%282%29-1%29%5E2+%2B+%281%29%5E2+
+hyp%5E2=%282+-2sqrt%282%29+%2B+1+%29+%2B+%281%29+
+hyp%5E2=4+-2sqrt%282%29+

so then +sin+A+=+opp%2Fhyp+ and +cos+A+=+adj%2Fhyp+ giving
+sin+A%2AcosA+=+%28opp%2Fhyp%29%28adj%2Fhyp%29+
+sin+A%2AcosA+=+%28opp%29%28adj%29%2Fhyp%5E2+
+sin+A%2AcosA+=+%28sqrt%282%29-1%29%281%29%2F%284+-2sqrt%282%29%29+
+sin+A%2AcosA+=+%28sqrt%282%29-1%29%2F%284+-2sqrt%282%29%29+



+sin+A%2AcosA+=+2sqrt%282%29%2F%2816-8%29+
+sin+A%2AcosA+=+2sqrt%282%29%2F8+
+sin+A%2AcosA+=+sqrt%282%29%2F4+ QED