Integrating with Trigonometric Identities (AQA A-Level Mathematics): Quizzes

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Integrating with Trigonometric Identities
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What is the first step in integrating using trigonometric identities?

Simplify with identities

Which identity is equivalent to tan⁡2θ+1\tan^2 \theta + 1?

sec⁡2θ\sec^2 \theta

What is ∫tan⁡2θ dθ\int \tan^2 \theta \, d\theta?

tan⁡θ−θ+c\tan \theta - \theta + c

What is ∫tan⁡θ dθ\int \tan \theta \, d\theta?

−ln⁡∣cos⁡θ∣+c-\ln |\cos \theta| + c

Which identity expresses sin⁡2θ\sin 2\theta in terms of sin⁡θ\sin \theta and cos⁡θ\cos \theta?

2sin⁡θcos⁡θ2 \sin \theta \cos \theta

What is ∫sin⁡θcos⁡θ dθ\int \sin \theta \cos \theta \, d\theta using the double angle formula?

−14cos⁡2θ+c\frac{-1}{4} \cos 2\theta + c

Express sin⁡2x\sin^2 x in terms of cos⁡2x\cos 2x.

12−12cos⁡2x\frac{1}{2} - \frac{1}{2}\cos 2x

What is ∫sin⁡2x dx\int \sin^2 x \, dx?

12x−14sin⁡(2x)+c\frac{1}{2}x - \frac{1}{4} \sin(2x) + c

Express cos⁡2x\cos^2 x in terms of cos⁡2x\cos 2x.

12cos⁡2x+12\frac{1}{2}\cos 2x + \frac{1}{2}

What is ∫cos⁡2x dx\int \cos^2 x \, dx?

12x+14sin⁡(2x)+c\frac{1}{2}x + \frac{1}{4} \sin(2x) + c

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