Question

Given 5\sinβ = \sin (2α +β), find the value of \dfrac{\tan (α +β)} {\tan \alpha }

Collected in the board: Trigonometry

Steven Zheng posted 2 months ago


Answer

\sin (2α +\beta)

=\sin(α +β )\cosα +\cos(α +β )\sinα

5\sinβ=5\sin[(α +β )-α ]

=5\cosα\sin(α +β )-5\sinα\cos(α +β)

\because 5\sinβ = \sin (2α +β)

\therefore 4\sin(α +β )\cosα = 6\cos(α +β )\sinα

\therefore \dfrac{\tan (α +β)} {\tan \alpha }

Steven Zheng posted 2 months ago

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