Question

*32. If theta is an acute angle and 2 sin theta - 1 = 0, find the value of 3 tan theta + 8 cos 2theta - 5.​

Answer 1

Answer:

$2 \sin(theta) = 1 \\ = > \sin(theta) = \frac{1}{2} = \sin( {30}^{0} ) \\ = > theta = {30}^{0} then \\ 3 tan(theta) + 8 \cos(2theta) - 5 = 3 \tan( {30}^{0} ) + 8 \cos(2 \times {30}^{0} ) - 5 = \frac{3}{ \sqrt{3} } + 8 \cos( {60}^{0} ) - 5 = \sqrt{3} + \frac{8}{2} - 5 = \sqrt{3} + \frac{8 - 10}{2} = \sqrt{3} + \frac{ - 2}{2} = \sqrt{3} - 1$

Answer 2

3tanθ + 8cos2θ - 5 = √3 - 1

for detailed solution you can see the attachment.

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