Question

Verify: [\sin \theta (1+\sin \theta)+\cos \theta(1+\cos \theta)]\cdotp [\sin \theta (1-\sin \theta)+\cos \theta(1-\cos \theta)] = \sin 2\theta

Collected in the board: Trigonometry

Steven Zheng posted 1 month ago


Answer

[\sin \theta (1+\sin \theta)+\cos \theta(1+\cos \theta)]\cdotp [\sin \theta (1-\sin \theta)+\cos \theta(1-\cos \theta)]

=( \sin \theta +\cos \theta +1)(\sin \theta +\cos \theta -1)

=(\sin \theta +\cos \theta )^2-1

=2\sin \theta \cos \theta

=\sin 2\theta

Steven Zheng posted 1 month ago

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