Question

If 5 sin theta - 12 cos theta = 0, then find the value of tan​

Answer 1

Given: 5 sin θ - 12 cos θ = 0

To find: The value of the tan θ

Solution: In mathematics, the branch which describes the angles of a triangle and sides of that triangle is termed trigonometry. The basic three functions of this trigonometry are cosine, sine, and tangent. All these functions are used to solve the problems related to trigonometry.

From above, we have

5 sin θ - 12 cos θ = 0

⇒ 5 sin θ = 12 cos θ

⇒ sin θ/ cos θ =12/5  [rearranging the sides]

⇒ tan θ = 12/5  [∵ tan θ = sin θ/ cos θ]

Hence the value of tan θ is 12/5.

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Answer 2

Appropriate Question :-

$\rm \: If \: 5sin\theta - 12cos\theta = 0, \: find \: the \: value \: of \: tan\theta$

$\large\underline{\sf{Given- }}$

$\rm \: 5sin\theta - 12cos\theta = 0$

$\large\underline{\sf{To\:Find - }}$

$\rm \: tan\theta$

$\large\underline{\sf{Solution-}}$

Given that,

$\rm \: 5sin\theta - 12cos\theta = 0$

can be rewritten as

$\rm \: 5sin\theta = 12cos\theta$

$\rm \: \dfrac{sin\theta }{cos\theta } = \dfrac{12}{5}$

$\rm\implies \:\rm \:\boxed{ \rm{ \: tan\theta = \dfrac{12}{5} \: }}$

$\rule{190pt}{2pt}$

$\boxed{ \rm{ \:Additional\:Information}}$

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{sin(90 \degree - x) = cosx}\\ \\ \bigstar \: \bf{cos(90 \degree - x) = sinx}\\ \\ \bigstar \: \bf{tan(90 \degree - x) = cotx}\\ \\ \bigstar \: \bf{cot(90 \degree - x) = tanx}\\ \\ \bigstar \: \bf{cosec(90 \degree - x) = secx}\\ \\ \bigstar \: \bf{sec(90 \degree - x) = cosecx}\\ \\ \bigstar \: \bf{ {sin}^{2}x + {cos}^{2}x = 1 } \\ \\ \bigstar \: \bf{ {sec}^{2}x - {tan}^{2}x = 1 }\\ \\ \bigstar \: \bf{ {cosec}^{2}x - {cot}^{2}x = 1 }\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$