cotA/1+cosecA-cotA/1-cosecA=k/cosA,then find the value of k
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Answered by
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Answer:
k = 2
Step-by-step explanation:
Multiply by cos A and factor out cot A. Also handier to change signs of numerator and denominator in second term:
k = cos A cot A ( 1 / ( cosec A + 1 ) + 1 / ( cosec A - 1 ) )
Change everything to cos A and sin A. Distribute the 1 / sin A (from the cot A) over the terms:
k = cos² A ( 1 / ( 1 + sin A ) + 1 / ( 1 - sin A ) )
= cos² A ( 1 - sin A + 1 + sin A ) / ( 1 - sin² A )
= cos² A ( 2 ) / cos² A
= 2
Anonymous:
Basically, the approach is change everything to cos and sin (remember cot = cos / sin and cosec = 1 / sin) then simplify. You might take different steps but you end up at the same place, needing to use cos^2 + sin^2 = 1 so that the final cancellation can happen. I hope this was helpful enough for you to copy or adapt to your needs.
Answered by
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