if a = sec x -tan x and b=cosec x +cot x the show that ab+a-b+1=0
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Answer:
Step-by-step explanation:
a = sec x - tan x
b = cosec x + cot x
Now,
ab + a - b + 1 = (sec x - tan x)(cosec x + cot x) + sec x - tan x - (cosec x + cot x) + 1
= sec x . cosec x + cosec x - sec x - 1 + sec x - tan x - cosec x - cot x + 1
= sec x . cosec x - tan x - cot x
= sec x . cosec x - (tan x + cot x)
= sec x . cosec x - (sin x/cos x + cos x/sin x)
= sec x . cosec x - [(sin^2 x + cos^2 x)/sin x . cos x]
= sec x . cosec x - [1/sin x . cos x]
= sec x . cosec x - sec x . cosec x
= 0
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