Question

) If 5 sin 0 - 12 cos 0 = 0 then find the value of sec 0.​

Answer 1

Step-by-step explanation:

Given:-

5 Sin θ - 12 Cos θ = 0

To find:-

Find the value of Sec θ ?

Solution:-

Given that

5 Sin θ - 12 Cos θ = 0

=> 5 Sin θ = 12 Cos θ

=> 5 Sin θ/ Cos θ = 12

=> Sin θ/ Cos θ = 12/5

=> Tan θ = 12/5

On squaring both sides then

=> ( Tan θ) ^2 = (12/5)^2

=> Tan^2 θ = 144/25

On adding 1 both sides then

=> 1 + Tan^2 θ = 1 + (144/25)

=> 1 + Tan^2 θ = (25+144)/25

=> 1 + Tan^2 θ = 169/25

We know that

Sec^2 A - Tan^2 A = 1

=> Sec^2 θ = 169/25

=> Sec θ = √(169/25)

=> Sec θ = 13/5

Answer:-

The value of Sec θ for the given problem is 13/5

Used formulae:-

• Tan A = Sin A/ Cos A

• Sec^2 A - Tan^2 A = 1