Question

solve this.........​

Answer 1

Question

If tan2° = x/y, find sec²88°/(1 + cot²88°)

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Answer

$\sf\frac{y^2}{x^2}$

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Explanation

First of all let's simplify $\sf\frac{sec^2(88^{\circ})}{1 + cot^2(88^{\circ})}$

We know that the relation between cot∅ and cosec∅ is given by the identity

1 + cot²∅ = cosec²∅

→ 1 + cot²88° = cosec²88°

Hence,

$\sf\frac{sec^2(88^{\circ})}{1 + cot^2(88^{\circ})}=\frac{sec^2(88^{\circ})}{cosec^2(88^{\circ})}$

Now, we know that tan∅ = sec∅/cosec∅

→ $\sf\frac{sec^288^{\circ}}{cosec^288^{\circ}} = tan^2(88^{\circ})$

Also, tan∅ = 1/tan(90 - ∅)

→ tan(88°) = 1/tan(2°)

→ tan²(88°} = 1/tan²(2°)

→ tan²(88°) = 1/(x/y)²

→ tan²(88°) = y²/x²

Hence, the answer is $\sf\frac{y^2}{x^2}$

Answer 2

Step-by-step explanation:

$\frac{ {sec}^{2}88 }{1 + {cot}^{2}2 } = \: \frac{ {cosec}^{2} 2}{ {cosec}^{2} 88} = \: \frac{ {cosec}^{2}2 }{ {sec}^{2}2 } \\ = \: \frac{ {cos}^{2}2 }{ {sin}^{2}2} \\ = {cot}^{2}2 = \frac{1}{ {tan}^{2}2 }$

${cot}^{2}2 \: = \frac{ {y}^{2} }{ {x}^{2} }$

answer of the question is y^2/x^2

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