  # Solve the equation for x if 0 s x < 2. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.)2 sin x — 3 cot x — 3 csсх 3D 0

Question
check_circleExpert Solution
Step 1

The given trigonometric equation is shown below.

Step 2

Write all the trigonometric function in terms of sine and cosine. help_outlineImage Transcriptionclose2sin x 3 cotx-3cscx =0 1 -3 cos x 2sin x-3 sin x sin x 3 -= 0 sinx 2sin -3 sin x Simplifying it 2sin2x3cosx-3 = 0 2(1-cos2x)-3 cosx-3=0 2 2 cos2 x3 cos x - 3 = 0 -2 cos2 x-3 cos x - 1= 0 2 cos2 3 cosx +1= 0 fullscreen
Step 3

The above equation is quadratic in cos x.

Now solve t... help_outlineImage Transcriptionclose2 cos2 x3 cos x 1= 0 Take cos x = u 2u3u1 0 -3+ v32 -4-2.1 и 2-2 -3t1 и %3 4 1 u-1 2 1 cos x 2 fullscreen

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### Trigonometry 