Question

If 5 sin theta - 12 cos theta=0, find the value of sec theta. ​

Answer 1

Answer:

Step-by-step explanation:

given- 5sina-12cosa=0

to find-sec a

5sina-12cosa=0

divide by cosa

5sina/cosa-12=0

5tana-12=0

5tana=12

squaring both sides

25tan^2a=144

tan^2a=144/25

we know 1+tan^2a=sec^a

sec^2a-1=144/25

sec^a=144/25+1

sec^a=169/25

seca=13/5

Answer 2

Given,

5 sinθ - 12 cosθ = 0

To find,

The value of secθ.

Solution,

• 5 sinθ - 12 cosθ = 0

• -12 cosθ will go from the left-hand side of the equation to the right-hand side of the equation and its sign would change from -12 cosθ to +12cosθ.

• 5 sinθ = 12 cosθ

         (sinθ/cosθ) = 12/5.

We know that sinθ/cosθ is tanθ, therefore we get,

⇒   tanθ = 12/5

1 +tan²θ = sec²θ

⇒   1 + (12/5)² = sec²θ

⇒   1 + 144/25 = sec²θ

⇒   (144+25)/25 = sec²θ

⇒   169/25 = sec²θ

⇒    secθ = √169/√25

⇒   secθ = 13/5.

Therefore the value of secθ is 13/5.