Question 94

What is the simplified value of (cosec A + sin A)(cosec A - sin A)?

Solution

Expression : $$(cosecA+sinA)(cosecA-sinA)$$

= $$(\frac{1}{sinA}+sinA)(\frac{1}{sinA}-sinA)$$

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

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

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

= $$cot^2A + cos^2A$$

=> Ans - (A)

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