Differentiate:\(\frac{d}{d\theta}(cos\theta-sin\theta)^2\)

1.	Differentiate:\(\frac{d}{d\theta}(cos\theta-sin\theta)^2\)
Answer» \(\frac{d}{d\theta}(cos\theta-sin\theta)^2\) = 2(cos θ - sin θ) \(\frac{d}{d\theta}(cos\theta-sin\theta)\) = 2(cos θ - sin θ) (-sinθ - cos θ) = -2(cos θ - sin θ) (cos θ - sin θ) = -2(cos θ - sin θ) (cos θ - sin θ) = -2 (cos²θ - sin²θ) = -2 cos 2θ

Answer»

\(\frac{d}{d\theta}(cos\theta-sin\theta)^2\) = 2(cos θ - sin θ) \(\frac{d}{d\theta}(cos\theta-sin\theta)\)

= 2(cos θ - sin θ) (-sinθ - cos θ)

= -2(cos θ - sin θ) (cos θ - sin θ)

= -2 (cos²θ - sin²θ)

= -2 cos 2θ

Discussion

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