Question 96

What is the simplified value of $$[{\frac{cosA}{(1-tanA)}+{\frac{sinA}{(1-cotA)}}}]^2$$ ?

Solution

Expression : $$[{\frac{cosA}{(1-tanA)}+{\frac{sinA}{(1-cotA)}}}]^2$$

= $$[(\frac{cosA}{1-\frac{sinA}{cosA}})+(\frac{sinA}{1-\frac{cosA}{sinA}})]^2$$

= $$[(\frac{cos^2A}{cosA-sinA})-(\frac{sin^2A}{cosA-sinA})]^2$$

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

= $$(\frac{(cosA-sinA)(cosA+sinA)}{cosA-sinA})^2$$

= $$(cosA+sinA)^2$$

= $$cos^2A+sin^2A+2sinAcosA$$

= $$1+sin2A$$

=> Ans - (B)

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