Question

# If $$\sin \theta - \cos \theta = 1$$, then the value of $$\sin^3 \theta - \cos ^3 \theta$$ is equal to

A
1
B
1
C
0
D
2
E
2

Solution

## The correct option is B $$1$$Given, $$\sin\theta-\cos\theta=1$$$$\sin^3\theta -\cos^3\theta=(\sin\theta-\cos\theta)(\sin^2\theta+\cos^2\theta+\sin\theta\cos\theta)$$$$=1(1+\sin\theta\cos\theta)$$$$=1+\sin\theta\cos\theta$$.........(i)$$[\because \sin\theta-\cos\theta=1]$$On squaring both sides,$$(\sin\theta-\cos\theta)^2=(1)^2$$$$\Rightarrow (\sin^2\theta+\cos^2\theta-2\sin\theta\cos\theta)=1$$$$\Rightarrow 1-2\sin\theta\cos\theta=1$$$$\sin\theta\cos\theta=0$$.........(ii)From Equations (ii) and (i), we get $$\sin^3\theta-\cos^3=1$$Mathematics

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