Question

tanx/secx-1 - sinx/1+cosx = 2cotx​

Answer 1

Tan x /secx-1 - sinx /1+ cos x =2 cotx

L.H.S.=Tanx/secx-1 - sinx /1+cos x

Sinx /cosx Upon 1/cosx-1 - Sinx /1+cos x ( Tan x = sin/cos and sec =1/ cos )

Taking L.c.m. of 1/cosx-1 = 1-cosx upon cos x

Sinx/cosx upon 1-cosx / cos x - sinx /1+cosx

cosx canceled

Sinx /1-cos x - sinx /1+cos x

Taking L.c.m.

sinx (1+cosx)- sinx (1-cosx) Upon (1-cosx) (1+cosx)

Then , sinx + sinx cosx - sinx + sinx cosx Upon 1-cos2

2sinxcosx upon sin2 ( sin2=1-cos2)

Sin canceled

Then 2cosx /Sinx = 2cot x = R.H.S.

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Answer 2

tep-by-step explanation:

tanx/secx-1 - sinx /1+cosx = 2 cotx

start with left side

tan/sec-1-sin/1+cos

(sin/cos)/[(1/cos)-1]-[sin/(1+cos)]

=(sin/cos)/[(1-cos)/cos]-[sin/(1+cos)]

=[(sin/(1-cos)]-[sin/(1+cos)]

LCD: (1-cos)(1+cos)

=[sin(1+cos)-sin(1-cos)]/(1-cos)(1+cos)

=[sin(1+cos)-sin(1-cos)]/(1-cos^2)

=[sin(1+cos)-sin(1-cos)]/(sin^2)

divide by sin

=[1+cos-1+cos)]/(sin)

=2cos/sin

=2 cotx

verified: left side=right side