Question

Given A is an acute angle and cosec A = √2, find the value of 2sin²A+3cot²A/(tan²A−cos²A).
$please \: answer \: correctly$
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Answer 1

Solution -

It is given that A is an acute angle.

•°• 0° < A < 90°

⠀

It is also given that,

➝ cosec A = √2

➝ cosec 45° = √2

➝ A = 45°

⠀

Now, we have to find the value of

• $\sf{\dfrac{2sin^2 A + 3cot^2A}{tan^2A - cos^2A}}$

⠀

We will put A = 45°

$\sf\dashrightarrow{\dfrac{2sin^2 45^{\circ} + 3cot^2 45^{\circ}}{tan^2 45^{\circ} - cos^2 45^{\circ}}}$

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Putting the trigonometric values

$\sf\dashrightarrow{\dfrac{2 \times (\dfrac{1}{\sqrt{2}})^2 + 3 \times (1)^2}{(1)^2 - (\dfrac{1}{\sqrt{2}})^2}}$

⠀

$\sf\dashrightarrow{\dfrac{2 \times \dfrac{1}{2} + 3}{1 - \dfrac{1}{2}}}$

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$\sf\dashrightarrow{\dfrac{1 + 3}{\dfrac{1}{2}}}$

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$\sf\dashrightarrow{4 \times \dfrac{2}{1}}$

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$\bf\dashrightarrow{\pink{8}}$

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Hence,

• The required value is 8.

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Answer 2

Solution-

•°• 0° < A < 90°

⠀

It is also given that,

➝ cosec A = √2

➝ cosec 45° = √2

➝ A = 45°

⠀

Now, we have to find the value of

$\sf{\dfrac{2sin^2 A + 3cot^2A}{tan^2A - cos^2A}}$

•

⠀

We will put A = 45°

ANSWER

$\sf\dashrightarrow{\dfrac{2sin^2 45^{\circ} + 3cot^2 45^{\circ}}{tan^2 45^{\circ} - cos^2 45^{\circ}}}$