Q.

cotθtanθ2tan2θ4tan4θ=

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a

4cot8θtan6θ

b

cot8θ+tan3θ

c

cot8θ+cot6θ

d

8θcot6θ

answer is D.

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Detailed Solution

cotθtanθ=1tanθtanθ=1tan2θtanθ=21tan2θ2tanθ=2tan2θ=2cot2θcotθtanθ2tan2θ4tan4θ=2cot2θ2tan2θ4tan4θ                         =2(cot2θ2tan2θ)4tan4θ  =4cot4θ4tan4θ=4(cot4θtan4θ)=8cot8θ.

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