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Q.

Lines L1and L2 have slopes m and n, respectively. Suppose L1 makes  twice as large angle with horizontal ( measured counter clockwise from the positive x-axis) as does L2 and L1 has 4 times the slope of L2. If L1 is not horizontal, then the value of the product mn equals ____

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answer is 2.

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Detailed Solution

Let m=tan2θ and n=tanθAnd m=4nand m≠0,∴  tan2θ≠0 ;∴ θ≠0tan2θ=4tanθ⇒2tanθ1−tan2θ=4tanθ⇒1=2−2tan2θ⇒2tan2θ=1⇒tan2θ=1/2⇒mn=tan2θ.tanθ=2tan2θ1−tan2θ=11−1/2=2
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