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101. sin (α + β) from Sine Rule; cos (α + β) from Cosine Rule

Published online by Cambridge University Press:  03 November 2016

A. G. Sillitto
A. G. Sillitto*
Affiliation:
Jordanhill College of Education, Glasgow
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Abstract

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Type
Class Room Notes
Information
The Mathematical Gazette , Volume 47 , Issue 359 , February 1963 , pp. 58
Copyright
Copyright © Mathematical Association 1963

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References

Notes

(i) The proofs hold for all acute angles α, β.

(ii) With angle ACB obtuse, the formulae for sin (α — β) and cos (α — β) are obtained similarly Again α, β must be acute, and consequently α — β also.

(iii) No. 1 is virtually the first proof given on p. 63 of the Associa-tion's Trigonometry Report, where explicit use is made of the formula a = b cos C + c cos A (which happens not to be included in the syllabus for the Scottish Certificate of Education!). The proof of No. 2 is a little simpler if this formula is not used.