Question

If 5sino - 12coso = 0, find the values of seco and coseco.

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Answer 1

Answer:

13/5,13/12

Step-by-step explanation:

5sino=12coso

5/12=coso/sino

5/12=coto

so we know that cot is base/height in right angle triangle.. so base is 5 and height is 12

so by using hyptonues (don't see the spelling) formula

hy^2 = b^2 + al^2

hy^2 =25+144

hy=13 ...

1/coso=seco , coso = base / hyptonues ..

hy/base= seco

13/5= seco

13/12=coseco

Answer 2

Answer:

• The value of sec θ is 13/5 and the value of cosec θ is 13/12.

Step-by-step explanation:

Given that:

• 5 sin θ - 12 cos θ = 0 _______(i)

To Find:

• The values of sec θ and cosec θ.

Finding the value of sec θ:

• According to the question.

⟶ 5 sin θ - 12 cos θ = 0

⟶ 5 sin θ = 12 cos θ

• Squaring both sides.

⟶ 25 sin² θ = 144 cos² θ

• We know: sin² θ = 1 - cos² θ

⟶ 25(1 - cos² θ) = 144 cos² θ

⟶ 25 - 25 cos² θ = 144 cos² θ

⟶ 144 cos² θ + 25 cos² θ = 25

⟶ 169 cos² θ = 25

⟶ (13 cos θ)² = (5)²

• Cancelling power both sides.

⟶ 13 cos θ = 5

⟶ cos θ = 5/13 _______(ii)

• We know: cos θ = 1/sec θ

⟶ 1/sec θ = 5/13

⟶ sec θ = 13/5

∴ The value of sec θ = 13/5

Finding the value of cosec θ:

• In equation (i).

⟶ 5 sin θ - 12 cos θ = 0

• Substituting the value of cos θ from eqⁿ (ii).

⟶ 5 sin θ - 12 × 5/13 = 0

⟶ 5 sin θ - 60/13 = 0

⟶ 5 sin θ = 60/13

⟶ sin θ = 60/(13 × 5)

⟶ sin θ = 12/13

• We know: sin θ = 1/cosec θ

⟶ 1/cosec θ = 12/13

⟶ cosec θ = 13/12

∴ The value of cosec θ = 13/12