Question

If 5 sin θ − 12 cos θ = 0 , the find tan θ .

Answer 1

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Answer 2

★Asked★

If 5 sin θ − 12 cos θ = 0 , the find tan θ .

★Solution★

$5\;sin\theta-12\;cos\theta=$

$\implies\frac{sin\theta}{cos\theta}=\frac{12}{5}$

$\implies \;tan\theta =\frac{12}{5}$

Taking recirprocals,

\cot\theta=\frac{5}{12}[/tex]

$</p><p>\text{Using,} \boxed{\bf\;cosec^2\theta-cot^2\theta=1}$$\implies\;cosec^2\theta=1+cot^2\theta$

$=1+\frac{25}{144}$

$=\frac{144+25}{144}$

$=\frac{169}{144}\implies\boxed{\bf\;cosec\theta=\frac{13}{12}}$