Question

find the value of 1+tan2 theta/1+cot2 theta ans tan2 theta

Answer 1

Answer:

$Value \: of \: \frac{1+tan^{2}\theta}{1+cot^{2}\theta}= tan^{2}\theta$

Step-by-step explanation:

$Value \: of \: \frac{1+tan^{2}\theta}{1+cot^{2}\theta}\\=\frac{sec^{2}\theta}{cosec^{2}\theta}$

$By \: trigonometric \: identities :\\i) 1+ tan^{2}A = sec^{2}A\\ii) 1+cot^{2}A = cosec^{2}A$

$=\frac{\frac{1}{cos^{2}\theta}}{\frac{1}{sin^{2}\theta}}\\=\frac{sin^{2}\theta}{cos^{2}\theta}$

$Since ,i) secA = \frac{1}{cosA}\\ii)cosecA = \frac{1}{sinA}$

$=tan^{2}\theta$

Therefore,

$Value \: of \: \frac{1+tan^{2}\theta}{1+cot^{2}\theta}= tan^{2}\theta$

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Answer 2

refer to the attachment