Question

the value of 1+sin theta - cos theta/1+sin theta+cos theta + 1+ sin theta + cos theta/1 +sin theta - cos theta is

Answer 1

Answer:

(1 +sin∅ - cos ∅) / (1=sin =cos∅)  +  (1 +sin∅ + cos∅) / (1 + sin∅ - cos∅)

=( 1 +sin∅ -cos∅)^2 + ( 1+ sin∅ +cos∅)^2  / ( 1+sin∅)^2 - cos^2∅)

=(1+sin)^2 - 2(1+sin∅).cos∅ + cos^2∅ + (1+sin∅)^2 - 2(1+sin∅)^2.cos∅ +cos^2∅  /1 +2sin∅ + sin^2∅ -cos^2∅

=2(1+2sin∅ +sin^2∅) + 2 cos^2∅  /2 sin∅ + 2 sin^2∅

=2 + 4 sin∅ +2sin^2∅ + 2cos^2∅  / 2 sin∅(1 +sin∅)

=2 + 4sin∅ + 2(sin^2∅ +cos^2∅)  /2sin∅(1 + sin∅)

=4 + 4sin∅ /2sin∅(1+sin∅)

=4(1+sin∅)  /  2 sin∅(1 + sin∅)

=1/sin∅