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| 1. |
Tany=3tanx , prove tan(x+y)=2sin2y/1+2cos2y |
| Answer» tan (x+y) = (2sin 2y) /(1+2cos2y)L.H.S :-tan (x+y)=(tan x +tan y ) / (1-tan x tan y)Substitute, the value of tan x with (tan y)/3=(tan y/3 +tany) / (1-tan y/3 • tan y)=(tan y + 3tan y) / (3-tan²y)=(4tan y) / (3- tan²y)=(4 sin y/cos y) / (3 - sin²y/cos²y)=(4sin y • cos y) / (2cos² y +cos² y -sin²y)= (2 sin 2y) / (1 + 1 - 2sin²y + cos 2y)= (2 sin 2y) / (1 + 2 cos 2y) ☑️☑️☑️☑️L.H.S =R.H.S ? Proved | |