Question 84

What is the value of (1+cosA)/(1-cosA)?

Solution

Expression : $$\frac{1 + cos A}{1 - cos A}$$

Multiplying numerator and denominator by $$(1 + cos A)$$

= $$\frac{1 + cos A}{1 - cos A}$$ $$\times \frac{1 + cos A}{1 + cos A}$$

= $$\frac{(1 + cos A)^2}{1 - cos^2 A} = \frac{(1 + cos A)^2}{sin^2 A}$$

= $$(\frac{1 + cos A}{sin A})^2 = (\frac{1}{sin A} + \frac{cos A}{sin A})^2$$

= $$(cosec A + cot A)^2$$

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What is the value of (1+cosA)/(1­-cosA)?