Question
Sat July 28, 2012 By: Sivendu Sivendu
 

Prove that tan50degree=tan40degree+2tan10degree.

Expert Reply
Sat July 28, 2012
tan 50 degree = tan (40+10) degree 
tan 50 degree = tan 40 + tan 10/1- tan 40 * tan 10 
(Since, tan (a + b )= tan a + tan b/1- tan a * tan b)
tan 50 (1-tan40*tan10)=tan 40 + tan 10
tan 50 ( 1 - tan (90 - 50)*tan 10 ) = tan 40 + tan 10
tan 50 (1 - cot 50 * tan 10 ) = tan 40 + tan 10 
tan 50 - tan 50 cot 50 tan 10 = tan 40 + tan 10
tan 50 -tan 10 = tan 40 + tan 10
tan 50 = tan 40 + tan 10 + tan 10
tan 50 degree = tan 40 degree + 2 tan 10 degree
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