Question

If sin theta = 4/5 , find the value of 4 tan theta - 5 cos theta /sec theta + 4 cot theta ​

Answer 1

Answer:

$\sin(x) = \frac{4}{5} \\ \cos(x) = \frac{3}{5} \tan(x) = \frac{4}{3} . \cot(x) = \frac{3}{4} . \sec(x) = \frac{5}{3} . \\ 4 \times \frac{4}{3} - 5 \times \frac{3}{5} \div \frac{5}{3} + 4 \times \frac{3}{4} \\ answer \: is \: \frac{3}{14}$

Answer 2

EXPLANATION.

⇒ Sin∅ = 4/5.

As we know that,

Sin∅ = perpendicular/hypotenuse.

By using Pythagoras theorem, we get.

⇒ H² = P² + B².

Put the value in equation, we get.

⇒ (5)² = (4)² + B².

⇒ 25 = 16 + B².

⇒ 25 - 16 = B².

⇒ 9 = B².

⇒ B = √9.

⇒ B = 3.

Sin∅ = perpendicular/hypotenuse = 4/5.

Cos∅ = base/hypotenuse = 3/5.

tan∅ = perpendicular/base = 4/3.

Cosec∅ = hypotenuse/perpendicular = 5/4.

Sec∅ = hypotenuse/base = 5/3.

Cot∅ = base/perpendicular = 3/4.

Value of = 4tan∅ - 5Cos∅/Sec∅ + 4Cot∅.

⇒ 4(4/3) - 5(3/5)/(5/3) + 4(3/4).

⇒ 16/3 - 3/5/3 + 3.

⇒ 16 - 9/3/5 + 9/3.

⇒ 7/3/14/3.

⇒ 7/3 X 3/14.

⇒ 7/14.

⇒ 1/2.