SSC CGL Tier-2 01-December-2016 Maths Question 86

Question 86

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

Solution

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

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

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

$$( \frac{1+cosĀ 22^\circ +sinĀ 22^\circ}{cosĀ 22^\circ})Ā $$ $$( \frac{cosĀ 22^\circ +sinĀ 22^\circ -1}{sin 22^\circ})$$

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

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



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