Question

cota+coseca-1/cota-coseca+1=coseca+cota

Answer 1

Answer:cosec A + cot A - 1 / cot A - cosec A + 1  

we know that,cosec ² A - cot ² A = 1  

substituting this in the numerator  

cosec A + cot A -(cosec ² A - cot ² A) / (cot A - cosec A + 1)  

x²-y²= (x+y)(x-y)  

cosec A + cot A - (cosec A + cot A) (cosec A - cot A) / (cot A - cosec A + 1)  

taking common  

(cosec A + cot A)(1-cosec A + cot A) / (cot A - cosec A + 1)  

cancelling like terms in numerator and denominator  

we are left with cosec A + cot A  

= 1/sin A + cos A/sin A  

= (1+cos A) / sin A

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