prove that tan(x+y)=tanx+tany/1-tanxtany
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Hey my dear friend here is your answer_____________
tan x+y = (tan x + tan y) / (1 - tan x tan y)
We already know (see trigonometry identities) that
cos (x+y) = cos x cos y - sin x sin y
and
sin (x+y) = sin x cos y + cos x sin y
So,
tan (x + y) = (sin x+y) / (cos x+y)
= (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)
Dividing both numerator and denominator by (cos x)(cos y), we get:
= ( sin x / cos x + sin y / cos y) / (1 - sin x sin y/(cos x cos y))
= (tan x + tan y) / (1 - tan x tan y).
Hence, the prof.
__________________________
Refer attached pic...
__________________________
Hope this answer will help u dear....
@Neha...
Hey my dear friend here is your answer_____________
tan x+y = (tan x + tan y) / (1 - tan x tan y)
We already know (see trigonometry identities) that
cos (x+y) = cos x cos y - sin x sin y
and
sin (x+y) = sin x cos y + cos x sin y
So,
tan (x + y) = (sin x+y) / (cos x+y)
= (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)
Dividing both numerator and denominator by (cos x)(cos y), we get:
= ( sin x / cos x + sin y / cos y) / (1 - sin x sin y/(cos x cos y))
= (tan x + tan y) / (1 - tan x tan y).
Hence, the prof.
__________________________
Refer attached pic...
__________________________
Hope this answer will help u dear....
@Neha...
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