Question

tan(45+x/2)=tanx+secx

Answer 1

LHS:tan(x2+π4)

=sin(x2+π4)cos(x2+π4)

=sin(x2)cos(π4)+cos(x2)sin(π4)cos(x2)cos(π4)−sin(x2)sin(π4)

=1√2sin(x2)+1√2cos(x2)1√2cos(x2)−1√2sin(x2)

=1√2(sin(x2)+cos(x2))1√2(cos(x2)−sin(x2))->factor out common factor

=1√2(sin(x2)+cos(x2))1√2(cos(x2)−sin(x2))-> cancel common factor

=sin(x2)+cos(x2)cos(x2)−sin(x2)

=sin(x2)+cos(x2)cos(x2)−sin(x2)⋅cos(x2)+sin(x2)cos(x2)+sin(x2)->multiply by conjugate

=sin2(x2)+2sin(x2)cos(x2)+cos2(x2)cos2(x2)−sin2(x2)

=[sin2(x2)+cos2(x2)]+2sin(x2)cos(x2)cos2(x2)−sin2(x2)

=1+2sin(x2)cos(x2)cos2(x2)−sin2(x2)

=1+sin2(x2)cos2(x2)

=1+sin2(x2)cos2(x2)

=1+sinxcosx

=1cosx+sinxcosx

=secx+tanx

=RHS

Answer 2

нσρє ιт нєℓρѕ уσυ....

мαяк мє αѕ вяαιиℓιєѕт..