Question

sin theta / cos theta (1- cot theta) + cos theta / sin theta ( 1- tan theta ) = 1 + sec theta * cosec theta
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Answer 1

Step-by-step explanation:

L.H.S

=Sin∅/cos∅ (1-cot∅) + cos∅/sin∅ (1-tan∅)

= tan∅(1-cot∅) + cot∅(1-tan∅)

= tan∅ - cot∅.tan∅ + cot∅ - cot∅.tan∅

= tan∅ +cot∅ +1

= Sin∅/cos∅ + cos∅/sin∅ +1

= (sin2∅ + cos2∅)/sin∅.cos∅ + 1

= 1/sin∅.cos∅ +1

= sec∅.cosec∅ +1