Question

$if \: cotv = 2x \div \sqrt{9 - {4x}^{2} } \\ \: then \: evaluate \\ 1)sinv + cosv \\ 2)cosecv - tanv$

Answer 1

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

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

✔ 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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GIVEN, Cot v = (2x)/{√(9-4x²)}

We also know, Cot v = Cos v/Sin v.

So, Cos v = 2x.

Sin v = √(9-4x²)

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(1) Sin v + Cos v

= √(9-4x²) + 2x

= 2x + √(9-4x²) [ANSWER]
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(2) Cosec v - Tan v

= 1/Sin v - 1/Cot v

= 1/√(9-4x²) - √(9-4x²)/2x [ANSWER]