What is tan2x if cosx=1-sinx ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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If we'll divide the constraint from enunciation by cos x, the expression will become

sin x + cos x=1

sin x/cos x + 1= 1/cos x

tan x + 1= 1/cos x

tan x= (1/cos x) -1

tan 2x=tan (x+x)=

tan 2x = (tan x+ tan x)/[1-(tan x)^2]

tan 2x =  2tan x/[1-(tan x)^2]

tan 2x = 2[(1/cos x) -1]/{1-[(1/cos x) -1]^2}

tan 2x= 2(1-cos x)/cosx /(2 - 1/cosx)(1/cos x)

tan 2x= 2(1-cos x)/(2 - 1/cosx)

tan 2x = 2cosx(1 - cos x)/(2cos x - 1)

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lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

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cosx=1-sinx

sinx = 1-cosx

devide the equation by cosx

tan = secx -1

tanx = secx - 1

we know that tan2x = 2tanx/(1-tan²x)

tan2x = 2(secx-1)/[1- (secx-1)²]

tan2x = 2(secx-1)/[1 -(sec²x-2secx+1)]

tan2x = 2(secx-1)/[1 -sec²x+2secx-1)] 

tan2x = 2(secx-1)/[2secx-sec²x]

tan2x = 2(secx-1)/secx(2-secx)

tan2x = 2(1-cosx)/cosx.secx(2-secx)

tan2x = 2(1-cosx)/(2-secx)

tan2x = 2cos(1-cosx)/(2cosx-1)

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