Math, asked by simi0412, 11 months ago

solve this.........​

Attachments:

Answers

Answered by Mankuthemonkey01
6

Question

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

\rule{100}2

Answer

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

\rule{100}2

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}

Answered by rani49035
1

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

hope this will help you

please follow me...

Similar questions