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Find, to 1 decimal place, the values of θ in the interval 0 ⩽ θ ⩽ 180° for which 4root3 sin (3theta + 20degrees) = 4 cos (3theta+ 20degrees)?

Make 3thetha + 20 = y So you’ll have: 4root3 siny = 4 cos y Then divide both sides by cos y So 4 root 3siny/cos y = 4cosy/cosy Siny/cosy = tan y and cosy/cosy = 1 Therefore: 4root 3 tan y = 4 Divide both sides by 4 So: root3 tan y = 1 So tan y = 1/root3 Change your intervals: 0<theta<180 => 0<3theta<540 => 0<3theta +20<560 y= 30,210,390,570 Let y = 3 theta+20 Theta = (y-20)/3 So plug each value into (y-20)/3 theta = 3.3, 63.3, 123.3, 183.3 Take any value under 180 degrees. So reject 183.3 degrees

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Hiral Haria
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