(Cosec x /cosec x - 1) +( cosec x / cosec x + 1) = sec 2 x
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Step-by-step explanation:
(cosec x /cosec x - 1) +( cosec x / cosec x + 1) = 2sec ²x
taking LHS
(cosec x /cosec x - 1) +( cosec x / cosec x + 1)
=[(cosec x *(cosec x + 1)) +(cosec x * (cosec x - 1)) ]/(cosec x+1)(cosec x-1)
=(cosec²x+cosec x+cosec²x-cosec x)/(cosec²x-1)
=(2 cosec² x)/cot² x
=(2* 1/sin² x)/(cos² x/sin² x)
=2/cos²x
=2 sec²x
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