Question

prove this sum........ and explain​

Answer 1

Answer:

in the form of X ok

l.h.s.= 1/(secx + tanx) -1/ coax

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

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

= cos²-1-sinx/ cosx (1+sinx)

= 1-sin²x-1-sinx/ cosx (1+sinx)

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

= - tanx

RHS,

1/cosx- 1/ (secx - tanx) ( simplifi in term of sin and cos and take LCM)

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

= 1-sinx-cos²x/ cosx(1-sinx)

=1 - sinx -(1-sin²x)/ cosx(1-sinx)

= sin²x-sinx/ cosx(1-sinx)

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

= - tanx

Step-by-step explanation:

put cos²x= 1- sin²x