Question 86

The value of the expression $$(1 + \sec 22^\circ + \cot 68^\circ)(1 - \cosec 22^\circ + \tan 68^\circ)$$is

Solution

$$(1 + \sec 22^\circ + \cot 68^\circ)(1 - \cosec 22^\circ + \tan 68^\circ)$$

$$(1 + \sec 22^\circ + \tan22^\circ)(1 - \cosec 22^\circ + \cot22^\circ)$$

$$(1 + \frac{1}{cos 22^\circ} + \frac{sin 22^\circ}{cos 22^\circ})(1 - \frac{1}{sin 22^\circ} +\frac{cos 22^\circ}{sin 22^\circ})$$

$$( \frac{1+cos 22^\circ +sin 22^\circ}{cos 22^\circ})$$ $$( \frac{cos 22^\circ +sin 22^\circ -1}{sin 22^\circ})$$

$$\frac{sin^2 22^\circ + cos^2 22^\circ + 2cos22^\circ \times sin22^\circ -1}{ cos 22^\circ sin 22^\circ }$$

$$\frac{1 + 2cos 22^\circ sin 22^\circ -1}{ cos 22^\circ sin 22^\circ }$$ = 2