Question

If 5 tanA = 4, then find the value of (5 sinA – 3 cosA)/(5 sinA + 2 cosA)

Answer 1

Step-by-step explanation:

5tan = 4

tanA=4/5

p=4 b=5

h=

$\sqrt{ {5 }^{2} + {4 }^{2} }$

$\sqrt{25 + 16}$

$\sqrt{41}$

SinA=

$4 \div \sqrt{41}$

cosA=

$5 \div \sqrt{41}$

5sinA-3cosA/5sinA+2cosA

$5 \times 4 \div \sqrt{41 } - 3 \times 5 \div \sqrt{41} \div 5 \times 4 \div \sqrt{41} + 2 \times 5 \div \sqrt{41}$

$20 \div \sqrt{41} - 15 \div \sqrt{41 } \div 20 \div \sqrt{41} + 10 \div \sqrt{41}$

$5 \div \sqrt{41} \times \sqrt{41} \div 30$

=1/6

Answer 2

Answer:

hey here is ur answer in above pics

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Step-by-step explanation:

your final answer is 1/6

pls note that here negative values are also possible after taking square roots on either sides but as tangent ratio is positive in nature ie as it lies in quadrant 1 the other must also be positive so as to satisfy required condition