Prove that `sec theta - cos theta = sin theta tan theta.` (2 marks)
Trigonometry, 2ADV T2 SM-Bank 42
Prove that
`(1 - sin^2 x cos^2 x)/(sin^2 x) = cot^2 x + sin^2 x`. (2 marks)
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Trigonometry, 2ADV T2 SM-Bank 41
Prove that
`(secx + tanx)(secx - tanx) = 1`. (2 marks)
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Trigonometry, 2ADV T2 2017 HSC 7 MC
Which expression is equivalent to `tan theta + cot theta`?
(A) `text(cosec)\ theta + sec theta`
(B) `sec theta\ text(cosec)\ theta`
(C) `2`
(D) `1`
Trigonometry, 2ADV T2 2004 HSC 8a
- Show that `cos theta tan theta = sin theta`. (1 mark)
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- Hence solve `8 sin theta cos theta tan theta = text(cosec)\ theta` for `0 ≤ theta ≤ 2pi`. (2 marks)
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Calculus, 2ADV C4 2010 HSC 5b
- Prove that `sec^2 x + secx tanx = (1 + sinx)/(cos^2x)`. (1 mark)
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- Hence prove that `sec^2 x + secx tanx = 1/(1 - sinx)`. (1 mark)
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- Hence, use the identity `int sec ax tan ax\ dx=1/a sec ax` to find the exact value of
`int_0^(pi/4) 1/(1 - sinx)\ dx`. (2 marks)
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