Question 79

What is the value of $$(sinA-2sin^3A)/(2cos^3A-cosA)$$?

Solution

Expression : $$(sinA-2sin^3A)/(2cos^3A-cosA)$$

= $$\frac{sinA}{cosA} \times \frac{1-2sin^2A}{2cos^2A-1}$$

$$\because$$ $$(sin^2A+cos^2A=1)$$

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

= $$tanA \times \frac{cos^2A-sin^2A}{cos^2A-sin^2A}$$

= $$tanA \times 1 = tanA$$

=> Ans - (D)

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