We have an answer to "Simple trigonometrysin⁡100∘sin⁡60∘+11+2sin⁡50∘=2sin⁡50∘"

luminarc24lry

Answered question

2022-05-02

Simple trigonometry

\frac{{\sin 100}^{\circ}}{{\sin 60}^{\circ}} + \frac{1}{1 + 2 {\sin 50}^{\circ}} = 2 {\sin 50}^{\circ}

2sze1c1se3nh

Beginner2022-05-03Added 17 answers

Divide by

2 {\sin 50}^{\circ}

\frac{{\cos 50}^{\circ}}{{\sin 60}^{\circ}} + \frac{1}{2 {\sin 50}^{\circ} + 2 - 2 {\cos 100}^{\circ}} = 1

{\cos 50}^{\circ} (2 {\sin 50}^{\circ} + 2 + 2 {\sin 10}^{\circ}) + {\sin 60}^{\circ} = 2 {\sin 60}^{\circ} ({\sin 50}^{\circ} + 1 + {\sin 10}^{\circ})

{\sin 100}^{\circ} + 2 {\cos 50}^{\circ} + {\sin 60}^{\circ} - {\sin 40}^{\circ} + {\sin 60}^{\circ} = {\cos 10}^{\circ} - {\cos 110}^{\circ} + 2 {\sin 60}^{\circ} - {\cos 50}^{\circ} - {\cos 70}^{\circ} {\sin 80}^{\circ} + 2 {\cos 50}^{\circ} - {\sin 40}^{\circ}

= {\cos 10}^{\circ} + {\cos 70}^{\circ} + {\cos 50}^{\circ} - {\cos 70}^{\circ}

{\sin 80}^{\circ} + {\sin 40}^{\circ} = {\cos 10}^{\circ} + {\sin 40}^{\circ}

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