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Rzqust [24]
3 years ago
11

GivenGiven 15 cot A = 8, find sin A and sec A.​

Mathematics
1 answer:
Leviafan [203]3 years ago
8 0

Answer:

sin A = \frac{15}{17}, \ sec A = \frac{17}8

Step-by-step explanation:

15cot A = 8\\\\cotA = \frac{8}{15}\\\\1 + cot^2A = cosec^2 A\\\\1 +  (\frac{8}{15})^2 = cosec^2 A\\\\1 +  \frac{64}{225} = cosec^2A\\\\\frac{225+64}{225} = cosec^2 A\\\\cosec^2 A = \frac{289}{225}\\\\cosec A = \frac{17}{15}\\\\That \ is,  \ \frac{1}{sin A} = \frac{17}{15}\\\\sin A = \frac{15}{17}

cot A = \frac{8}{15}\\\\\frac{cos A}{sinA} = \frac{8}{15}\\\\cos A = \frac{8}{15} \times sin A = \frac{8}{15} \times \frac{15}{17} = \frac{8}{17}\\\\\frac{1}{cosA} = \frac{17}{8}\\\\sec A = \frac{17}{8}

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