Question

Evaluate 1 + tan square A by 1 + cot square A

Answer 1

Step-by-step explanation:

1+tan²A/1+cot²A

=sec²A/cosec²A

=1/cos²A×sin²A

=tan²A

Answer 2

The required value is $tan^2A$

Step-by-step explanation:

To Evaluate : $\dfrac{1+tan^2A}{1+cot^2A}$

Now as we know

$1+tan^2\theta = sec^2\theta \text{ and } 1+cot^2\theta= cosec^2\theta$

also we have     $\dfrac{sinA}{cosA} = tanA$

and

$sec\theta=\dfrac{1}{cosA} \\\\ cosec\theta = \dfrac{1}{sin\theta}$

So by using trigonometric identities we get

$\dfrac{1+tan^2A}{1+cot^2A} = \dfrac{sec^2A}{cosec^2A} =\dfrac{\dfrac{1}{cos^2A} }{\dfrac{1}{sin^2A}} = \dfrac{sin^2A}{cos^2A} = tan^2A$

Hence ,the required value is $tan^2A$

#Learn more

Prove that tan∅/(1-cot∅) +cot∅/(1-tan∅)=1+tan∅+cot∅

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