Question

$If \: \frac{cos^{2} \theta}{cos^{2} \theta - cos^{2} \theta} = 3, \: and \: 0\ \textless \ \theta \ \textless \ 90, \: then \: the \: value \: of \: \theta \: is: \\ a. \: 60 \:\:\:\:\:\: b.\: 45 \:\:\:\:\: c. \: 30 \:\:\:\:\:\: d. \: 40.$

Answer 1

HELLO DEAR,

i think something is mistake in your questions

right questions is like that:-

$\frac{ {cos}^{2} theta }{ {cot}^{2} theta - {cos}^{2} theta} = 3 \\solutions:- let theta=alpha [tex] \frac{ {cos}^{2} \alpha }{ {cot}^{2} \alpha - {cos}^{2} \alpha } = 3 \\ \\ = {cos}^{2} \alpha = 3 {cot}^{2} \alpha - 3 {cos}^{2} \alpha \\ \\ = 4 {cos}^{2} \alpha = 3 {cot}^{2} \alpha \\ \\ 4 {cos}^{2} \alpha = 3 \times \frac{ {cos}^{2} \alpha }{ {sin}^{2} \alpha } \\ \\ 4 = \frac{3}{ {sin}^{2} \alpha } \\ \\ {sin}^{2} \alpha = \frac{3}{4} \\ \\ {sin}^{2} \alpha = { (\frac{ \sqrt{3} }{2} })^{2} \\ \\ sin \alpha = \frac{ \sqrt{3} }{2} \\ \\ {sin} \alpha = sin60 \\ \\ \alpha = 60$

. hence option (a) 60 is correct
I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hola bro

( cos²∅ ) / ( cot²∅ - cos²∅ ) = 3

cos²∅ = 3cot²∅ - 3cos²∅

4cos²∅ = 3cot²∅

cos²∅/cot²∅ = ¾

sin²∅ = 3/4

taking roots in both sides ...

sin∅ = √3 / 2

We know that sin 60° = √3 / 2

sin 60° = sin ∅

so ,

∅ = 60°

Hope it helps.