Question

Find approximate solution for the equation in the interval 0<_ x <_ pi. round to three decimal places. tanx=5 sin x

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Answer 1

Answer D.

Explanation:

0, 1.369

Answer 2

d. 0, 1.369

Explanation:

Given:

The equation is:
`\tan x =5\sin x................(0\leq x\leq \pi)`

Adding
`-5\sin x` on both sides, we get

`\tan x - 5\sin x=0`

Using the identity
`\tan x=(\sin x)/(\cos x)`, we get

`(\sin x)/(\cos x)-5\sin x=0`

Factoring out
`\sin x`, we get

`\sin x((1)/(\cos x)-5)=0\\\\\therefore \sin x=0\ or\ (1)/(\cos x)-5=0\\\\x=\sin^(-1) (0)\ or\ \cos x=(1)/(5)\\\\x=0\ or\ x=\cos^(-1) ((1)/(5))\\\\x=0\ or\ x=1.3694\approx 1.369(\textrm{Round to 3 decimal places})`

Therefore, the solution of the given equation is either 0 or 1.369.

The correct choice is d.