sec $70^{o}$ sin $20^{o}$ + cos $20^{o}$ cosec $70^{o}$ = ?

(a) 0 (b) 1 (c) -1 (d) 2

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Solution

$s e c 70^{o} s i n 20^{o} + c o s 20^{o} c o s e c 70^{o}$

$= \frac{s i n 20^{o}}{c o s 70^{o}} + \frac{c o s 20^{o}}{s i n 70^{o}}$

$= \frac{s i n (90^{o} - 70^{o})}{c o s 70^{o}} + \frac{c o s (90^{o} - 70^{o})}{s i n 70^{o}}$

$= \frac{c o s 70^{o}}{c o s 70^{o}} + \frac{s i n 70^{o}}{s i n 70^{o}}$ = 1+1 = 2

Hence, the correct choice is (d).

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