Question

Sin a by 1 - cos a minus 1 - cos a by sin a multipy cos a by 1- sin a minus 1-sina by cos a

Answer 1

Answer:

4

Step-by-step explanation:

1. consider sinA /(1-cos A ) -(1-cos A )/ sinA

by taking LCM

= [ sin²A -(1-cosA)² ] / sinA(1-cosA)

= [ sin²A - 1 -cos² A +2cosA ] / sinA (1-cosA)

= [ -cos²A -cos²A +2cos A] / sinA ( 1-cos A)

= [ -2cos²A +2cosA ] /sinA (1-cosA)

= 2cosA [ 1-cosA] / sinA(1-cosA)

= 2 cosA/sinA

=2cotA

2. consider cosA / (1-sinA) - (1-sinA)/cosA

= [ cos²A -1-sin²A +2sinA] / cosA(1-sinA)

= [-sin²A-sin²A +2sinA] /cosA (1-sinA)

= [ -2sin²A+2sinA] /cosA (1-sinA)

= 2sinA (1-sinA) / cosA(1-sinA)

= 2sin A /cosA

= 2tanA

.•. [ sinA/(1-cosA) - (1-cosA)/sinA][ cosA/(1-sinA) - (1-sinA)/cosA]

=2cotA ×2tanA

=4