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1.7.11 Differentiating trigonometric functions (A-level only)

Medium
1234
Question 3

For a real variable ttt, use the quotient rule and the known derivatives of sin⁡t \sin t\,sint and cos⁡t \cos t\,cost to demonstrate that:

a.
ddt(tan⁡t)=sec⁡2t \frac{d}{dt}(\tan t) = \sec^2 t dtd​(tant)=sec2t
[3]
b.
ddt(sec⁡t)=sec⁡ttan⁡t \frac{d}{dt}(\sec t) = \sec t \tan t dtd​(sect)=secttant
[3]
c.
ddt(cot⁡t)=−csc⁡2t \frac{d}{dt}(\cot t) = -\csc^2 t dtd​(cott)=−csc2t
[3]
d.
ddt(csc⁡t)=−csc⁡tcot⁡t \frac{d}{dt}(\csc t) = -\csc t \cot t dtd​(csct)=−csctcott
[3]

1.7.11 Differentiating trigonometric functions (A-level only) Questions

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