Question

Simplest form of 1+tan^2A/
1 + cot^2A is​

Answer 1

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Answer 2

The simplest form for the given expression is $\frac{1+tan^2A}{1+cot^2A}=tan^2A$

Step-by-step explanation:

Given expression is $\frac{1+tan^2A}{1+cot^2A}$

To find the simplest form of the given expression :

• $\frac{1+tan^2A}{1+cot^2A}$

• $=\frac{sec^2A}{cosec^2A}$  ( by using the identities $1+tan^2A=sec^2A$  and $1+cot^2A=cosec^2A$  )

• $=\frac{(\frac{1}{cos^2A})}{cosec^2A}$ ( by using the identity $sec^2A=\frac{1}{cos^2A}$  )

• $=\frac{1}{cos^2A}\times (\frac{1}{cosec^2A})$

• $=\frac{1}{cos^2A}\times (sin^2A)$  ( by using the identity $cos^2A=\frac{1}{cosec^2A}$  )

• $=\frac{sin^2A}{cos^2A}$  ( by using the identity $\frac{sin^2A}{cos^2A}=tan^2A$  )  

• $=tan^2A$

Therefore the given expression becomes $\frac{1+tan^2A}{1+cot^2A}=tan^2A$

The simplest form for given expression is $\frac{1+tan^2A}{1+cot^2A}=tan^2A$