Chapter 7: Q. 3 (page 495)

$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$ .

Short Answer

Expert verified

$\tan \frac{θ}{2} = \frac{1 - \cos θ}{\underset{⏝}{\sin θ}}$ .

Step by step solution

Step 1. Given Data

The given incomplete equation is

$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$

Step 2. Explanation

Use tangent formula

$\tan \frac{θ}{2} = \frac{\sin \frac{θ}{2}}{\cos \frac{θ}{2}} \tan \frac{θ}{2} = \frac{2 \sin^{2} \frac{θ}{2}}{2 (\sin \frac{θ}{2}) (\cos \frac{θ}{2})} \tan \frac{θ}{2} = \frac{1 - \cos (2 \frac{θ}{2})}{\sin (2 \frac{θ}{2})} \tan \frac{θ}{2} = \frac{1 - \cos θ}{\sin θ}$

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$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$ .

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

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tanθ2=1-cosθ_____.

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

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$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$ .