Question

if 5 sinø-12 cos ø=0 find the values of sec ø and cosec ø​

Answer 1

Answer:

$\rm \cosec θ=\dfrac{13}{12}$

$\rm \sec θ = \dfrac{13}{5}$

Step-by-step explanation:

We have,

$\rm 5 \sin θ -12 \cos θ=0$

dividing by $\rm \cos θ$

$\rm 5 \tan θ -12 =0$

$\rm \tan θ = \dfrac{12}{5}$

$\rm \tan ^2 θ = \dfrac{144}{25}$

$\rm \tan ^2 θ +1= \dfrac{144}{25}+1$

$\rm \sec ^2 θ = \dfrac{144+25}{25}$

$\rm \sec θ = \sqrt{\dfrac{169}{25}}$

$\rm \sec θ = \dfrac{13}{5}$

$\rm 5 \sin θ -12 \cos θ=0$

dividing by $\rm \sin θ$

$\rm 5 -12 \cot θ=0$

$\rm \cot θ=\dfrac{5}{12}$

$\rm \cot ^2 θ=\dfrac{25}{144}$

$\rm \cot ^2 θ+1=\dfrac{25}{144}+1$

$\rm \cosec ^2 θ=\dfrac{25+144}{144}$

$\rm \cosec ^2 θ=\dfrac{169}{144}$

$\rm \cosec ^2 θ=\dfrac{169}{144}$

$\rm \cosec θ=\sqrt{\dfrac{169}{144}}$

$\rm \cosec θ=\dfrac{13}{12}$