Question

Without using trigonometrical tables, evaluate: 5 cos 0° - 2 sin 30° + √3 cos 30° divided by tan 30° x tan 60° x cos 60°

Answer 1

The value of given equation = 11

Given:

5 cos 0° - 2 sin 30° + √3 cos 30° divided by tan 30° x tan 60° x cos 60°

To find:

Without using trigonometrical tables, evaluate above equation.

Formula used:

tan$\theta$ = $\frac{sin\theta}{cos\theta}$

sin$\theta$ = cos (90-$\theta$)

Explanation:

First we take denominator.

     tan 30° x tan 60° x cos 60°

       = $\frac{sin30}{cos30}$ x $\frac{sin60}{cos60}$ x cos 60°

        = $\frac{sin30}{cos30}$  x sin(60)

         = $\frac{sin30}{cos30}$ × cos (90-60)

         = sin30

The value of numerator = 5 cos 0° - 2 sin 30° + √3 cos 30°

 cos 0° = 1      sin 30° =$\frac{1}{2}$    cos 30°= $\frac{\sqrt{3} }{2}$

So, 5 cos 0° - 2 sin 30° + √3 cos 30°= 5×1 - 2× $\frac{1}{2}$ +$\sqrt{3}$×$\frac{\sqrt{3} }{2}$

                                                          = 5.5

  $\frac{5.5}{sin 30}$ = 5.5×2 = 11

So the value of given equation = 11

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