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If theta lies in the first quardrant and...

If `theta` lies in the first quardrant and `costheta=(8)/( 17 )`, then find the value of `cos(30^(@)+theta)+cos(45^(@)-theta)+cos(120^(@)-theta)`.

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To solve the problem, we need to find the value of \( \cos(30^\circ + \theta) + \cos(45^\circ - \theta) + \cos(120^\circ - \theta) \) given that \( \cos \theta = \frac{8}{17} \) and \( \theta \) lies in the first quadrant. ### Step 1: Find \( \sin \theta \) We know that: \[ \sin^2 \theta + \cos^2 \theta = 1 \] ...
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