The approximate value of tan ($44^\circ$30'), given that $1^\circ$ = 0.0175c, is ______.

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The approximate value of tan ($44^\circ$30'), given that $1^\circ$ = 0.0175c, is 0.9825. Explanation: $1^\circ$ = 0.0175c and tan ($44^\circ$30') Here, f(x) = tan x f'(x) = sec2x take 45 and h = ($\frac{1}{2}$)^circ $\therefore$ h = (-$\frac{1}{2}$)^\circ = $\frac{1}{2}$ xx 0.0175 = − 0.00875 and, f(a) = tan $45^\circ$ = 1 f'(a) = sec2 $45^\circ$ = (sqrt2)^2 = 2 The formula for approximation is, $\therefore$ f(a + h) = f(a) + h f'(a) f($44^\circ$30') = `f(45^\circ) + ($\frac{1}{2}$)^\circ xx f'(45^\circ)` = 1 + (−0.00875) $\times$ 2 = 1 − 0.0175 = 0.9825

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