Question 96

$$2 - (cosA + sinA)^2$$ is equal to

Solution

Expression : $$2 - (cosA + sinA)^2$$

= $$2 - (cos^2A + sin^2A + 2sinAcosA)$$

Using, $$(cos^2A + sin^2A = 1)$$ ----------(i)

= $$2 - (1 + 2sinAcosA)$$

= $$1 - 2sinAcosA$$

Again using equation (i), we get :

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

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

=> Ans - (D)

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