Question

Find the general solution : tanx = sinx​

Answer 1

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

Given Trigonometric equation is

$\rm \: tanx = sinx$

can be rewritten as

$\rm \: \dfrac{sinx}{cosx} = sinx$

$\rm \: sinx = sinx \: cosx$

$\rm \: sinx - sinx \: cosx = 0$

$\rm \: sinx(1 \: - \: cosx) = 0$

$\rm\implies \:sinx = 0 \: \rm\implies \:\boxed{ \rm{ \:x = n\pi \: \forall \: n \in \: Z \: }}$

Or

$\rm\implies \:1 - cosx = 0$

$\rm \: cosx = 1$

$\rm \: cosx = cos0$

$\rm\implies \:x = 2m\pi \: \pm \: 0 \: \: \forall \: m \in \: Z$

$\rm\implies \:\boxed{ \rm{ \:x = 2m\pi \: \: \forall \: m \in \: Z \: }}$

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

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}$

Answer 2

Step-by-step explanation:

sinx=tanx

sinx= sinx /cosx

cosx=1

x=cos−1 (1)

x=0°

So, x=2nπ+0°

∴ x=2nπ

General solution of sinx=tanx is cosx

Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type

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