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Standard XII

Mathematics

General Solution of Trigonometric Equation

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Question

From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance $d$ apart are $α$ and $β .$ The height of the lighthouse is

\frac{d tan α}{tan α + tan β}

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\frac{d}{cot α + cot β}

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\frac{d tan β}{tan α + tan β}

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\frac{d cot α}{cot α + cot β}

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Solution

The correct option is B $\frac{d}{cot α + cot β}$

$cot α = \frac{x}{h}, cot β = \frac{d - x}{h} h cot α = x, h cot β = d - x h = \frac{d}{cot α + cot β}$

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From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance d apart are α and β. The height of the lighthouse is

The correct option is B dcotα+cotβ cotα=xh,cotβ=d−xhhcotα=x,hcotβ=d−xh=dcotα+cotβ

From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance $d$ apart are $α$ and $β .$ The height of the lighthouse is

The correct option is B $\frac{d}{cot α + cot β}$

$cot α = \frac{x}{h}, cot β = \frac{d - x}{h} h cot α = x, h cot β = d - x h = \frac{d}{cot α + cot β}$