Question

if cosec tita=3x , cot tita =3/x , then find the value of (x2-1/x2)

Answer 1

$\bold{TRIGONOMETRY \:\: - \:\: FACTS}$


✔ Trigonometry is the study of relationships between the sides and the angles of a triangle. 

✔ The general trigonometric ratios are sin theta, cos theta, tan theta, sec theta, cosec theta and cot theta. 

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We all know a triangle has three parts : base, height and hypotenuse.

✔ Sin theta = height/hypotenuse. 

✔ Cos theta = base/hypotenuse. 

✔ tan theta = height /base. 

✔ cot theta = base/height. 

✔ sec theta = hypotenuse/base. 

✔ cosec theta = hypotenuse/height. 

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$\underline\bold{\huge{ANSWER \: :}}$

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Given, cosec theta = 3x

Also, given, cot theta = 3/x

We know, cosec²theta - cot²theta = 1

So, (3x)² - (3/x)² = 1

=> 9 x² - 9/x² = 1

=> 9 (x² - 1/x²) = 1

=> x² - 1/x² = 1/9 [ANSWER]