smc-1044-30-Trig

Proof, EXT2 P2 2022 HSC 13b

The numbers , for integers , are defined as

These numbers satisfy the relation , for . (Do NOT prove this)

Use mathematical induction to prove that , for all integers . (4 marks)

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Mean mark 58%.

Proof, EXT2 P2 2019 HSC 14c

Show that . (2 marks)

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Use mathematical induction to prove that, for all ,

. (2 marks)

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	$$

ii.

♦ Mean mark 45%.





	$$

Proof, EXT2 P2 2009 HSC 8a

Using the substitution $$ , or otherwise, show that

$ $ (2 marks)

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Use mathematical induction to prove that, for integers ,

$ $ (3 marks)

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Show that $$ (2 marks)

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Hence find the exact value of
(2 marks)

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$ $

ii.

	$$
	$$


	$$

$ $

	$ $
	$ $
	$ $
	$$


	$$

iii. $$

iv.

Proof, EXT2 P2 2012 HSC 16b

Show that for and . (1 mark)

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Use mathematical induction to prove

for all positive integers . (3 marks)

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Find . (1 mark)

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ii.

iii.

Proof, EXT2* P2 2006 HSC 5d

Use the fact that
to show that

(1 mark)

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ii.