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QLDMath MethodsQuick questions

Unit 2: Calculus

Quick questions on Trigonometric identities (QCE Math Methods Unit 2)

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is express in one function?
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sin⁡2θ=1−cos⁡2θ\sin^2 \theta = 1 - \cos^2 \theta, and cos⁡2θ=1−sin⁡2θ\cos^2 \theta = 1 - \sin^2 \theta. Useful for rewriting an expression in a single trig function before solving.
What are difference of squares?
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1−sin⁡2θ=(1−sin⁡θ)(1+sin⁡θ)=cos⁡2θ1 - \sin^2 \theta = (1-\sin\theta)(1+\sin\theta) = \cos^2\theta.
What is combine over a common denominator?
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1cos⁡θ−cos⁡θ=1−cos⁡2θcos⁡θ=sin⁡2θcos⁡θ=sin⁡θtan⁡θ\frac{1}{\cos\theta} - \cos\theta = \frac{1 - \cos^2\theta}{\cos\theta} = \frac{\sin^2\theta}{\cos\theta} = \sin\theta \tan\theta.

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