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Question

The value of (cot x2tan x2)2 (1-2 tan x cot 2x) is


A

1

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B

2

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C

3

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D

4

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Solution

The correct option is B

4


We have,

(cot x2tanx2)2 (12 tan x cot 2x)(cot2 x22 cot x2 tan x2+tan2 x2){12 tan x(cot2x12 cot x)}

(cot2 x22+tan2x2) {1tan x(cot2x1cot x)}(cot2 x2+tan2 x22) (1cot xtan xcot x)(cot2 x2+tan2 x21)(tan2 x)(cot2 x2+tan2 x22) (2 tan x21tan2 x9)2

=11tan2(x2)2(4+4 tan4 x28 tan2 x2)=1(1tan2 x2)2 (48 tan2 x2+4 tan2 x2)=4(1tan2 x2)2 {(tan2 x2)22(tan2 x2+1)}=4(tan2 x21)2(1tan2 x2)2
= 4


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