If tan A = 1√3, find the value of 1 - ^2 A/1 + ^2 A. A is acute.

3/5. tan A = 1√3 means A = 30°, so sin A = 1/2, sin^2 A = 1/4. 1 - 1/41 + 1/4 = 3/4/5/4 = 3/5.

If tan $A = \frac{1}{3}$ , find the value of $\frac{1 - s i n ^{2} A}{1 + s i n ^{2} A}$ .
A is acute.

Class 10Trigonometric IdentitiesTrigonometry

tan

A = \frac{1}{3}

means

A = 30

deg, so sin

A = \frac{1}{2}

, si

n^{2} A = \frac{1}{4} . \frac{1 - \frac{1}{4}}{1 + \frac{1}{4}} = \frac{3/4}{5/4} = \frac{3}{5}

Answer: A)

\frac{3}{5}

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