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NSWMaths Extension 1Trigonometric Functions (ME-T1, T2, T3)

Quick questions on Sum and difference identities for sin, cos and tan: expansions, simplifications and exact values

5short 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 are double-angle formulas?
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The double-angle formulas are not separate facts to memorise; they are the sum formulas with B=AB = A:
What are half-angle formulas?
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Rearranging the cos⁡2θ\cos 2\theta forms gives the power-reduction identities, and hence the half-angle formulas:
What are exact values for non-standard angles?
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The standard angles 0,30,45,60,90∘0, 30, 45, 60, 90^\circ have well-known exact values:
What is tangent sum with zero denominator?
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tan⁡(45∘+45∘)\tan(45^\circ + 45^\circ) has 1−1⋅1=01 - 1 \cdot 1 = 0 in the denominator; the identity is undefined and you must reason via sin⁡/cos⁡\sin/\cos directly.
What is an inefficient decomposition?
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sin⁡105∘=sin⁡(60+45)∘\sin 105^\circ = \sin(60 + 45)^\circ, not sin⁡(75+30)∘\sin(75 + 30)^\circ in the cleanest form. Choose decompositions into two standard angles.

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