Question 52

Solve the following.
$$\frac{2 \sin 22^\circ}{\cos 68^\circ} - \frac{2 \cot 75^\circ}{5 \tan 15^\circ} - \frac{8 \tan 45^\circ \tan 20^\circ \tan 40^\circ \tan 50^\circ \tan 70^\circ}{5}$$

Solution

$$\frac{2sin22^{0}}{cos68^{0}}-\frac{2cot75^{0}}{5tan15^{0}}-\frac{8tan45^{0}tan20^{0}tan40^{0}tan50^{0}tan70^{0}}{5}$$

$$\frac{2sin22^{0}}{cos(90 - 22)}-\frac{2cot(90 - 15)}{5tan15^{0}}-\frac{8tan45^{0}tan(90 - 70)tan(90 - 50)tan50^{0}tan70^{0}}{5}$$

$$\frac{2sin22^{0}}{sin22^{0}}-\frac{2tan15^{0}}{5tan15^{0}}-\frac{8tan45^{0}cot50^{0}cot70^{0}tan50^{0}tan70^{0}}{5}$$

$$2-\frac{2}{5}-\frac{8tan45^{0}}{5}$$

$$2-\frac{2}{5}-\frac{8}{5}$$ = 0


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