1. Use the compound angle formulae to expand and simplify:
a
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cos (60° + B)
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b
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tan (A + )
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c
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sin (A − 90°)
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2. By expressing each angle as a sum or difference e.g. 75° = 45° + 30°, and using the special triangles, where necessary, evaluate as a surd:
a cos 75° b tan 75° c sin 105° d cos 120° e sin 15° f tan 120°
3. Find the value of cos 2A if sin A = 0.4 and A is an acute angle.
4. Find the value of tan 2B if tan B = 1.5.
5. Write the following sums as products. i.e. Factorise
a
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sin 45° + sin 30°
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b
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cos 60° − cos 45°
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c
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cos 60° + cos 30°
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d
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cos 7x + cos 3x
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e
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sin 4x + sin 2x
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f
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sin 5x − sin x
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6. Write the following products as sums:
a
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2 sin A sin 2B
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b
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2 sin 47°cos 23°
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c
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2cos 5θ cos 3θ
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d
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2 cos sin
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e
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2 sin 5x / 2 sin 3x / 2
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f
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sin 3cos 2
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7. Show that cos 2A = 1 − 2sin2 A
8. Write 2 cos 3D sin D as the sum of two trig functions.