Question

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If 5 sine - 12 cos 0 = 0 then find the value of sec 0​

Answer 1

Ans--> Secθ = 13 / 5

I think question is like this

If 5Sinθ - 12 Cosθ = 0 then find the value of Secθ.

Solution---> ATQ,

5Sinθ - 12 Cosθ = 0

=> 5 Sinθ = 12 Cosθ

=> Sinθ / Cosθ = 12 / 5

=> tanθ = 12 / 5

We have an identity ,

1 + tan²θ = Sec²θ

=> Sec²θ = 1 + tan²θ

Putting tanθ = 12 / 5 , we get

= 1 + ( 12 / 5 )²

= 1 + (144 / 25)

= ( 25 + 144 ) / 25

=> Sec²θ = 169 / 25

=> Secθ = √(169/25)

=> Secθ = 13 / 5

Additional information --->

(1) Sin²θ + Cos²θ = 1

(2) 1 + Cot²θ = Cosec²θ