UPSKILL MATH PLUS

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9. Explain the given trigonometric equation by matching correct options

Answer variants:

$\frac{4 (\frac{\cos X}{\sin X}) - \cos X}{4 (\frac{\cos X}{\sin X}) + \cos X}$

$\frac{\cos X (\frac{4}{\sin X} - 1)}{\cos X (\frac{4}{\sin X} + 1)}$

$\frac{(4 \times \frac{1}{\sin X} - 1)}{(4 \times \frac{1}{\sin X} + 1)}$

$\frac{(4 \times \frac{1}{\cos X} - 1)}{(4 \times \frac{1}{\cos X} + 1)}$

$\frac{4 (\frac{\sin X}{\cos X}) - \cos X}{4 (\frac{\sin X}{\cos X}) + \cos X}$

$\frac{(\frac{4}{\sin X} - 1)}{(\frac{4}{\sin X} + 1)}$

Prove that

$\frac{4 \cot X - \cos X}{4 \cot X + \cos X}$

$=$

$\frac{4 cosec X - 1}{4 cosec X + 1}$ .

Proof:

LHS

$=$

$\frac{4 \cot X - \cos X}{4 \cot X + \cos X}$

$=$

$\frac{4 cosec X - 1}{4 cosec X + 1}$

$=$ RHS

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