Question 94

What is the simplified value of (cos A + sin A)(cot A + tan A)?

Solution

Expression : (cos A + sin A)(cot A + tan A)

= $$(cosA+sinA)(\frac{cosA}{sinA}+\frac{sinA}{cosA})$$

= $$(cosA+sinA)(\frac{sin^2A+cos^2A}{sinAcosA})$$

= $$\frac{cosA+sinA}{sinAcosA}$$

= $$\frac{cosA}{sinAcosA}+\frac{sinA}{sinAcosA}$$

= $$\frac{1}{sinA}+\frac{1}{cosA}=cosecA+secA$$

=> Ans - (A)

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