Question

यदि 15 cot A = 8 हो तो सिद्ध करे कि sinA=15/17 एवं SecA = 17/8

Answer 1

15 cot A = 8

Cot A = 8/15

b/p = 8k/15k

b = 8k

p = 15k

=> h = √p²+b²

=> h= √225k² + 64k²

=> h = √289k²

=> h = 17k

Now,

Sin A = p/h

Sin A = 15k/17k

Sin A = 15/17

Again,

Sec A = h/b

Sec A = 17k/8k

Sec A = 17/8

Proved....

Answer 2

Step-by-step explanation:

$15 \: cot \: A = 8 \\ \implies \: cot \: A = \frac{8}{15} \\ \implies \: tan \: A = \frac{15}{8} \\ sec ^{2} A = 1 + tan^{2} A = 1 + ({ \frac{15}{8} })^{2} \\ = 1 + \frac{225}{64} = \frac{64 + 225}{64} = \frac{289}{64} \\ \huge \fbox {sec A = \frac{17}{8}} \\ \implies \: cos A = \frac{8}{17} \\ sin ^{2} A = 1 - cos ^{2} A \\ = 1 - ( { \frac{8}{17} )}^{2} = 1 - \frac{64}{289} \\ = \frac{289 - 64}{289} = \frac{225}{289} \\ \huge \fbox {sin A = \frac{15}{17} }\\ \\\huge \fbox {Thus\: proved}$