Question

prove that √ cos ec 0 -1 / cos ec 0 + 1 = 1/ sec0 + tan 0​

Answer 1

hey mate

here's the solution....

(I AM USING @ INSTEAD OF 0)

LHS:

=>√(cosec @-1)/(cosec @+1)

rationalising the denominator with (cosec @-1)

=>√(cosec @-1)/(cosec @+1)*(cosec @-1)/(cosec @-1)

=>√(cosec @-1)²/√(cosec @-1)*((cosec @+1)

=>(cosec @-1)/√(cosec² @-1)

=>(cosec @-1)/√cot² @

=>(cosec @-1)/cot @

=>cosec @/cot # - 1/cot @

=>sec @ - tan @

rationalising the denominator with

sec @+tan @

=>sec @ - tan @*sec @+tan @/sec @+tan @

=>sec ²@ -tan @/sec @+tan @

=>1/sec @+tan @

hence proved...

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