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Prove: tan 70° = tan 20° + 2tan 50°

Prove: tan 70° = tan 20° + 2tan 50°
asked 15.5k views
0 votes
Prove:
tan 70° = tan 20° + 2tan 50°

asked
User Koes Bong
by
8.1k points

2 Answers

5 votes
As we all know,
According to the trigonometric identity,
tan70=tan(20+50)
tan70=(tan20+tan50)/1-tan20tan50
tan70-tan20tan50tan70=tan20+tan50
Also tan70tan20=tan70cot70=1
Hence
tan70-tan50=tan20+tan50
So tan70=tan20+2tan50
Hope this helps :) :)
answered
User Ayman Sharaf
by
8.4k points
4 votes
tan(70-20)=tan50
tan70-tan20/1+tan20 tan70=tan50
tan20 tan70=cot70 tan70=1
tan70-tan20/2=tan50
tan70-tan20=2tan50
tan70=tan20+2tan50
answered
User Lithicas
by
9.1k points
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