Question

(cosec 0 - sec ) (cot 8 – tan 0) = (cosec 0 + sec 0) (sec 0 cosec 0 - 2)
Please answer
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Answer 1

Step-by-step explanation:

LHS

( cosec theta - sec theta)(cot theta - tan theta)

= (1/sin theta - 1/cos theta) ( cos theta/sin theta - sin theta/cos theta)

= (cos theta - sin theta)/sin theta cos theta ×

(cos²theta-sin²theta)/sin theta cos theta

= (cos theta - sin theta) × ( cos²theta - sin²theta)/ sin ²theta cos ²theta

= (cos theta - sin theta) ² × (cos theta+ sin theta)/sin ²theta cos ²theta

= ( 1- 2cos theta sin theta) ×( cos theta+ sin theta)/(sin theta cos theta)(sin theta cos theta)

= (cosec theta sec theta - 2)(cosec theta+ sec theta)

prooved