if 5 sin A-12 cos A=0 then cot A
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Answer:
5sinθ−12cosθ=0
\implies\frac{sin\theta}{cos\theta}=\frac{12}{5}⟹
cosθ
sinθ
=
5
12
\impliest\;tan\theta =\frac{12}{5}\impliesttanθ=
5
12
\text{Taking recirprocals,}Taking recirprocals,
\cot\theta=\frac{5}{12}cotθ=
12
5
\text{Using,}Using,
\boxed{\bf\;cosec^2\theta-cot^2\theta=1}
cosec
2
θ−cot
2
θ=1
\implies\;cosec^2\theta=1+cot^2\theta⟹cosec
2
θ=1+cot
2
θ
=1+\frac{25}{144}=1+
144
25
=\frac{144+25}{144}=
144
144+25
=\frac{169}{144}=
144
169
\implies\boxed{\bf\;cosec\theta=\frac{13}{12}}⟹
cosecθ=
12
13
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