Question

If sin Ø=4/5
then find the value of

4 tan Ø– 5cosØ/
sec Ø + 4cotØ​

Answer 1

Answer:

$\frac{1}{2}$

Step-by-step explanation:

sin∅ = $\frac{4}{5}$

∴ The triangle is a 3,4,5 pythagorean triplet

[Refer Diagram attached below]

tan∅ = $\frac{4}{3}$

cos∅ = $\frac{3}{5}$

sec∅ = $\frac{5}{3}$

cot∅ = $\frac{3}{4}$

Now, 4tan∅ - 5cos∅ / sec∅ + 4cot∅

⇒ $\frac{4(\frac{4}{3}) - 5(\frac{3}{5})}{\frac{5}{3} + 4(\frac{3}{4})}$

⇒ $\frac{\frac{16}{3} - 3}{\frac{5}{3} + 3}$

⇒ $\frac{1}{2}$

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Answer 2

Step-by-step explanation:

sin theta =4/5 = opposite/hypotenuse

By Pythagoras theorem,

adjacent = 3 [Pythagorean triplets]

therefore, tan theta = opposite/adjacent= 4/3

cos theta = adjacent/hypotenuse = 3/5

sec theta = hypotenuse/adjacent = 5/3

cot theta = adjacent/opposite = 3/4

4(4/3) - 5(3/5)

5/3 + 4(3/4)

16/3 - 3

5/3 + 3

16-9

3

5+9

3

7/14 = 1/2

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