0000:00:00:00:00Start7Number 7ExplanationGiven the trigonometric ratios of two acute angles AAA and BBB with sinA=513\sin A = \frac{5}{13}sinA=135 and cosB=817\cos B = \frac{8}{17}cosB=178. How many of the following four statements are true based on the information above? (1)tanA+tanB=1920\text{(1)} \quad \tan A + \tan B = \frac{19}{20}(1)tanA+tanB=2019(2)cosAsinB+cosBsinA=220221\text{(2)} \quad \cos A \sin B + \cos B \sin A = \frac{220}{221}(2)cosAsinB+cosBsinA=221220(3)tanAtanB=2532\text{(3)} \quad \frac{\tan A}{\tan B} = \frac{25}{32}(3)tanBtanA=3225(4)sinAcosBsinBcosA=29\text{(4)} \quad \frac{\sin A \cos B}{\sin B \cos A} = \frac{2}{9}(4)sinBcosAsinAcosB=92000111222333444
7Number 7ExplanationGiven the trigonometric ratios of two acute angles AAA and BBB with sinA=513\sin A = \frac{5}{13}sinA=135 and cosB=817\cos B = \frac{8}{17}cosB=178. How many of the following four statements are true based on the information above? (1)tanA+tanB=1920\text{(1)} \quad \tan A + \tan B = \frac{19}{20}(1)tanA+tanB=2019(2)cosAsinB+cosBsinA=220221\text{(2)} \quad \cos A \sin B + \cos B \sin A = \frac{220}{221}(2)cosAsinB+cosBsinA=221220(3)tanAtanB=2532\text{(3)} \quad \frac{\tan A}{\tan B} = \frac{25}{32}(3)tanBtanA=3225(4)sinAcosBsinBcosA=29\text{(4)} \quad \frac{\sin A \cos B}{\sin B \cos A} = \frac{2}{9}(4)sinBcosAsinAcosB=92000111222333444
