without-using-calculator-or-table-find-the-exact-value-of-sin-tan-1-1-2-

Question Number 10873 by Saham last updated on 28/Feb/17

without using calculator or table, find the exact value of :

\sin [\tan^{- 1} (\frac{1}{2})]

Answered by fariraihmudzengerere75@gmail.c last updated on 28/Feb/17

A n s w e r . \sin [\tan^{- 1} (x)] = x / \sqrt{(1 + x \frac{2}{})}

\sin [\tan^{- 1} (1 / 2)] = \frac{1 / 2}{\sqrt{1 + (1 / 2) \frac{2}{}}}

= \frac{1 / 2}{\sqrt{1 + 1 / 4}}

= \frac{1 / 2}{\sqrt{5 / 4}}

= (1 / 2) / \sqrt{5 / 4}

= (1 / 2) \times \frac{\sqrt{4}}{\sqrt{5}}

= \frac{1}{\sqrt{5}}

= \frac{\sqrt{5}}{5}

Commented by Saham last updated on 28/Feb/17

God bless you sir .

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