Question

Find the exact value of
​

Answer 1

Answer:

Given 7cot theta = 24

Then  cot theta = 24 / 7  = adj side / opp side

Then By Phythagorus Theorem,

(Adj Side)^2 + (Opp Side)^2 = (Hyp Side)^2

7^2 + 24^2 = x^2

x^2 = 625

x = $\sqrt{625}$

x = 25

Therefore Hypotenuse side = 25

Cos theta = 24 / 25

Now $\sqrt{1-cos theta / 1 + cos theta}$ =  $\sqrt{1-24/25}$ / $\sqrt{1+24/25}$

                                              = $\sqrt{25-24 / 25}$ / $\sqrt{25+24 / 25\\}$

                                              = $\sqrt{1/25}$ / $\sqrt{49/25}$

                                              $\sqrt{(1/5)^{2} }$ / $\sqrt{(7/5)^{2} }$

Square And root Gets Cancelled

Now The Equation Remains ,

         $\sqrt{1-cos theta / 1 + cos theta}$  = 1/5  / 7/5

                                                   = 1/5 * 5/7

                                                   = 1/7

 

Therefore ,  $\sqrt{1-cos theta / 1 + cos theta}$ = 1/7

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