Additional Trigonometric Identities (Exercises)

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au
and

Department of Mathematics
University of Wisconsin, Madison
Madison, WI 53706 USA
ram@math.wisc.edu

Last updates: 2 March 2010

Additional Trigonometric Identities (Exercises)

	Prove that arcsinhx=logx+x2+1.
	Prove that arcsinhx1-x2=arctanhx .
	Prove that arctanhx=12log1+x1-x .
	Prove that arccoshx=logx+x2-1 .
	Prove that cos2x=cos2x-sin2x .
	Prove that cos2x=2cos2x-1 .
	Prove that cos2x=1-2sin2x .
	Prove that sin2x=2sinxcosx .
	Prove that cosh2x=cosh2x+sinh2x .
	Prove that cosh2x=2cosh2x-1 .
	Prove that cosh2x=1+2sinh2x .
	Prove that sinh2x=2sinhxcoshx .
	Prove that 1-tanh2x=sech2x .
	Prove that coth2x-1=cosech2x .
	Prove that 1+tan2x=sec2x .
	Prove that cot2x+1=cosec2x .

References [PLACEHOLDER]

[BG] A. Braverman and D. Gaitsgory, Crystals via the affine Grassmanian, Duke Math. J. 107 no. 3, (2001), 561-575; arXiv:math/9909077v2, MR1828302 (2002e:20083)

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