Question 89

If cos3A = X, then value of X?

Solution

Expression : cos3A = X

= $$cos(2A+A)$$

= $$cos(2A)cosA-sin(2A)sinA$$

= $$(2cos^2A-1)cosA - (2sinAcosA)sinA$$

= $$2cos^3A-cosA - (sin^2A)2cosA$$

= $$2cos^3A-cosA- 2cosA(1-cos^2A)$$

= $$2cos^3A-cosA-2cosA+2cos^3A$$

= $$4cos^3A-3cosA$$

=> Ans - (A)

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