# First Year Math Trigonometric Identities

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$1. Prove thatv) \cos \left(270^{\circ}+\theta\right)=\sin \theta$

$3. Prove that:ii) \cos \left(\alpha+45^{\circ}\right)=\frac{1}{\sqrt{2}}(\cos \alpha-\sin \alpha)$

$2. Express the following sums or differences as products:ii) \sin 8 \theta-\sin 4 \theta$

$Example 5: If \alpha \beta \gamma are the angles of \triangle A B C prove that:i) \tan \alpha+\tan \beta+\tan \gamma=\tan \alpha \tan \beta \tan \gamma$

$Prove the following identities:3. \frac{\sin 2 \alpha}{1+\cos 2 \alpha}=\tan \alpha$

$9. If \sin \alpha=\frac{4}{5}< and \sin \beta=\frac{12}{13}< where \frac{\pi}{2} \alpha \pi and \frac{\pi}{2} \beta \pi . Findii) \cos (\alpha+\beta) In which rants do the terminal sides of the angles of measures (\alpha+\beta) and (\alpha-\beta) lie?$