MathematicsIf 05sec⁡θ-12cos⁡ecθ=0 , then find the values of sec θ , cos θand sin θ

$If 05 \sec θ - 12 \cos ecθ = 0, then find the values of sec θ, cos θand sin θ$

A
$secθ = \frac{13}{5}, cos θ = \frac{5}{13}, sin θ = \frac{12}{13}$
B
$secθ = \frac{5}{12}, cos θ = \frac{13}{5}, sin θ = \frac{12}{13}$
C
$secθ = \frac{5}{13}, cos θ = \frac{13}{5}, sin θ = \frac{13}{12}$
D
None of the above

Solution:

secθ = \frac{1}{cos θ} and cosecθ = \frac{1}{sin θ}

5 secθ - 12 cosecθ = 0

5 cosθ - 12 sinθ = 0

tanθ = \frac{12}{5}

tanθ = \frac{perpendicular}{base}

(perpendicular)^{2} + (base)^{2} = (hypotenuse)^{2}

(12)^{2} + (5)^{2} = (hypotenuse)^{2}

(hypotenuse)^{2} = 169

hypotenuse = 13

Hence,

secθ = \frac{13}{5}, cos θ = \frac{5}{13}, sin θ = \frac{12}{13}

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