Question

If sec x + tan x =m prove that sin x = m^2-1/m^2+1

Answer 1

Step-by-step explanation:

given,

m=secx+tanx

RHS

m²-1/m²+1

=(secx+tanx)²-1/(secx+tanx)²+1

=sec²x+tan²x+2secxtanx-1/sec²x+tan²x+2secxtanx+1

=(sec²x-1)+tan²x+2secxtanx/(tan²x+1)+sec²x+2secxtanx

=tan²x+tan²x+2secxtanx/sec²x+sec²x+2secxtanx

=2tan²x+2secxtanx/2sec²x+2secxtanx

=tanx(tanx+secx)/secx(secx+tanx)

=tanx/secx

=(sinx/cosx)×cosx

=sinx