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Question

The value of α lying between [0,π] for which the inequality tanα>tan3α is valid, is

A
(0,π4)(π2,3π4)
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B
(0,π2)(π2,3π4)
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C
(0,π3)(π3,π2)
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D
(0,π4)(π4,3π4)
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Solution

The correct option is A (0,π4)(π2,3π4)
We have : tanα>tan3α+
tanαtan3α>0tanα(1tan2α)>0
(tanα)(tanα+1)(tanα1)<0
So using wavy curve method tanα(,1)(0,1)


α(0,π4)(π2,3π4)

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