The correct option is A a cosα+bcosβ+ccosγ From figure #160;In OLA; #160;cosα #160; = AL / a and #160;α #160; = AL / x ⇒ AL=ac ...

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Chain Rule of Differentiation

AL+BM+CN is e...

Question

$A L + B M + C N$ is equal to

a cos α + b cos β + c cos γ

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a sin α + b sin β + c sin γ

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x cos α + y cos β + z cos γ

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x sin α + y sin β + z sin γ

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Solution

The correct option is A $a cos α + b cos β + c cos γ$
From figure
In $△ O L A;$ $cos α = \frac{A L}{a}$ and $cot α = \frac{A L}{x}$
$\Rightarrow A L = a cos α = x cot α$ .... $(1)$
In $△ O M B;$ $cos β = \frac{B M}{b}$ and $cot β = \frac{A M}{y}$
$\Rightarrow B M = b cos β = x cot β$ ... $(2)$
In $△ O N C;$ $cos γ = \frac{C N}{c}$ and $cot γ = \frac{C N}{z}$
$\Rightarrow C N = c cos γ = z cot γ$ ... $(3)$
From $(1), (2)$ and $(3)$
$A L + B M + C N = a cos α + b cos β + c cos γ$

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