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A ladder problem reduces to: if cos $A = \frac{m}{n}$ for an acute angle A, express tan A in terms of $m$ and $n$ .
Which is correct?

Class 10Trigonometric IdentitiesTrigonometry

A $\frac{n ^{2} - m ^{2}}{m}$
B $\frac{n ^{2} - m ^{2}}{n}$
C $\frac{m}{n ^{2} - m ^{2}}$
D $\frac{n}{n ^{2} - m ^{2}}$

Step-by-Step Solution

cos

A = \frac{m}{n}

, so sin

A = 1 - \frac{m ^{2}}{n ^{2}} = \frac{n ^{2} - m ^{2}}{n}

. tan

A

= sin A/cos

A = \frac{n ^{2} - m ^{2} / n}{m / n} = \frac{n ^{2} - m ^{2}}{m}

.

Answer: A)

\frac{n ^{2} - m ^{2}}{m}

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