Question

Tan(45+x)=sec2x+tan 2x

Answer 1

LHS = Tan(45° + x )

=(Tan45° +Tan45°)/(1-Tanx.Tan45°)

=(Tanx + 1)/( 1- Tanx )

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

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

=(sinx +cosx )(cosx - sinx)/(cosx -sinx)²

=(sin²x -cos²x)/(1-sin2x)

=cos2x/(sin2x -1)

=1/(sin2x - 1)/cos2x

=1/(tan2x - sec2x )

=(tan2x + sec2x )= RHS

Answer 2

Answer:

tan2x + sec2x

Step-by-step explanation:

tan(45 + x) = tan(90 + 2x/2)

we know that:-

tan2x = 2tanx/1-tan^2(x)

tanx = -cot2x + cosec2x

so

tan(90 + 2x/2) = -cot(90 + 2x) + cosec(90 + 2x)

-------"-------"--- = tan2x + sec2x

tan(45 + x) = tan2x + sec2x