Question

(1+cosx+sinx)/(1+cosx-sinx)=(1+sinx)/cosx

Answer 1

Answer:

Step-by-step explanation:

LHS

(1+cosx+sinx)/(1+cosx-sinx)

=(1/cosx+cosx/cosx+sinx/cosx)/(1/cosx+cosx/cosx-sinx/cosx)

[Dividing both numerator and denominator with cosx]

=(1/cosx+1+sinx/cosx)/(1/cosx+1-sinx/cosx)

=(secx+1+tanx)/(secx+1-tanx)

={(secx+tanx)+1}/{secx+1-tanx}

={secx+tanx+(sec²x-tan²x)}/{secx+1-tanx}           [sec²x-tan²x = 1]

={secx+tanx+(secx+tanx)(secx-tanx)}/{secx+1-tanx}

=[(secx+tanx){1+(secx-tanx)}]/[1+secx-tanx]

={(secx+tanx)(1+secx-tanx)}/(1+secx-tanx)

=secx+tanx

=(1/cosx)+(sinx/cosx)

=(1+sinx)/cosx  = RHS [Proved]