Introduction of Trigonometry — Maths STD 10 — Question
CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
Question
Simplest form of $\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}$ is _______.
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Answer
Simplest form of $\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}$ is $\tan^2\text{A}$. Solution:
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}=\Big(1+\frac{\sin^2\text{A}}{\cos^2\text{A}}\Big)$
$\Big(1+\frac{\cos^2\text{A}}{\sin^2\text{A}}\Big)$
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}=\Big(\frac{\sin^2\text{A}+\cos^2\text{A}}{\cos^2\text{A}}\Big)\Big(\frac{\sin^2\text{A}}{\sin^2\text{A}+\cos^2\text{A}}\Big)$
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}=\frac{\sin^2\text{A}}{\cos^2\text{A}}$
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}=\tan^2\text{A}$
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