Question

cosec A / cosec A - 1 - cosec A / 1 - cosec A = 2 / cos^2 A​

Answer 1

Answer:

Step-by-step explanation:

LHS:

=cosec A/cosec A-1  -   cosec A/1-cosec A

=cosec A/cosec A-1   -   (-cosec A/cosec A-1)

=cosec A/cosec A-1   +   cosec A/cosec A-1

=cosec A + cosec A/cosec A-1        [BY TAKING LCM]

=2 cosec A/cosec A-1

=(2/sin A)/(1/sin A - 1)                          [cosec A=1/sin A]

=2/sin A  /   1-sin A/sin A

=2/sin A   *     sin A/1-sin A

=2/1-sin A

=2/1-sin A   *    1+sin A/1+sin A

=2(1+sin A)/(1-sin A)(1+sin A)

=2(1+sin A)/1-sin^2 A

=2(1+sin A)/cos^2 A                           [1-sin^2 A= cos^2 A]