(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to:
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Correct answer: C
Explanation
The correct answer is Option 3 i.e 2
(1 + sec 20° + cot 70°)(1 - cosec 20° + tan 70°)
= (1 + sec 20° + tan 20°)(1 - cosec 20° + cot 20°)
Let 20° = x
= (1 + sec x + tan x)(1 - cosec x + cot x)
= (1 + 1/cos x + sin x/cos x)(1 - 1/sin x + cos x/sin x)
= [(sin x + cos x + 1)/cos x] [(sin x + cos x - 1)/sin x]
= [(sin x + cos x)2 - 12]/cos x sin x
= (1 + 2sin x cos x - 1)/cos x sin x
= 2