Question

3) If cosa= 8/17

then find the value of

3 sinA - 5 cosA
3 sinA + 7 COSA​

Answer 1

$\sin(a) = \sqrt{1 - \frac{ {8}^{2} }{ {17}^{2} } } \\ \\ \sin(a) = \sqrt{ \frac{289 - 64}{289} } \\ \\ \sin(a ) = \frac{15}{17} \\ hence \: now \\ \\ 3 \sin(a) - 5 \cos(a ) = 3 \times \frac{15}{17} - 5 \times \frac{8}{17} \\ \\ \ = \frac{45}{17} - \frac{40}{17} \\ \\ = \frac{45 - 40}{17} \\ \\ = \: \: \: \: \: \: \: \: \: \: \frac{5}{17} \\ \\ 3 \sin(a) + 7 \cos(a) = 3 \times \frac{15}{17} + 7 \times \frac{8}{17} \\ \\ = \frac{45}{17} + \frac{56}{17} \\ \\ = \frac{45 + 56}{17} \\ \\ = \frac{101}{17}$

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Answer 2

Answer:

3 sinA - 5 cosA = 5/17

3 sinA + 7 COSA = 8/17

Step-by-step explanation:

cos A = 8/17

cos A = B/H

sin A = P/H

H²=P²+B²

(17)²=P²+ (8)²

289-64=P²

P² = 225

P=15

sin A = 15/17

3 sin A - 5 cos A = 3X15/17 - 5X8/17

= 45/17 - 40/17

= 5/17

3 sin A + 7 cos A = 3X15/17 + 7x5/17

= 45/17 + 35/17

= 80/17