Question

Show that 3tanx=2+Sinx has solution

Answer 1

we have to show that 3tanx = 2 + sinx has solution.

we know, tanx ∈ R and sinx ∈ [-1, 1]

if tanx > 1 then, 3tanx > 3

and 3tanx = 2 + sinx > 3

⇒ sinx > 1 [ which is impossible]

but when choose tanx = 1

then, 3tanx = 2 + sinx = 3

sinx = 1 = sin(π/2)

⇒x = π/2 hence solution is possible

so, solution of 3tanx = 2 + sinx is possible when

when equation satisfied their properties.

we have to show it has solution, better to solve it by graph.

draw graph of LHS = 3tanx

and then draw graph of 2 + sinx [ just shift 2 unit above of sinx graph from the mean position as shown in 1st figure ]

see 2nd figure, here it is clearly shown point of intersection of two graphs.

hence, 3tanx = 2 + sinx has solution

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Answer 2

$\huge\mathbb\green{Answer:-}$

we have to show that 3tanx = 2 + sinx has solution.