Question

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The value of 1/1+cot2 A ​

Answer 1

Step-by-step explanation:

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Answer 2

The value of $\dfrac{1}{1+\cot^2 A}$ $=\sin^2 A$

Step-by-step explanation:

We have,

$\dfrac{1}{1+\cot^2 A}$

To find, the value of $\dfrac{1}{1+\cot^2 A}$ = ?

∴ $\dfrac{1}{1+\cot^2 A}$

Using the trigonometric identity,

$\csc^2 A-\cot^2 A=1$

⇒ $\csc^2 A=1+\cot^2 A$

∴ $\dfrac{1}{1+\cot^2 A}$

= $\dfrac{1}{\csc^2 A}$

Using the trigonometric identity,

$\sin A=\dfrac{1}{ \csc A}$

$=\sin^2 A$

∴ The value of $\dfrac{1}{1+\cot^2 A}$ $=\sin^2 A$

Hence, the value of $\dfrac{1}{1+\cot^2 A}$ $=\sin^2 A$