Compute the exact value of $\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$ without a calcuator?

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Compute the exact value of $\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$ without a calcuator?

$\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$

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Answer 1 · 2017-09-23T17:06:26

See explanation.

Explanation:

$\frac{tan 220 - sin 220}{tan 220 \cdot sin 220} = \frac{tan 220}{tan 220 \cdot sin 220} - \frac{sin 220}{tan 220 \cdot sin 220} =$ $(tan220-sin220)/(tan220*sin220)=tan220/(tan220*sin220)-sin220/(tan220*sin220)=$

$\frac{1}{sin 220} - \frac{1}{tan 220} = \frac{1}{sin 220} - \frac{cos 220}{sin 220} =$ $1/sin220-1/tan220=1/sin220-cos220/sin220=$

$\frac{1 - cos 220}{sin 220} = \frac{1 - cos (180 + 40)}{sin (180 + 40)} =$ $(1-cos220)/sin220=(1-cos(180+40))/sin(180+40)=$

$\frac{1 + cos 40}{- sin 40}$ $(1+cos40)/(-sin40)$

Finding the exact value of the expression is not possible, but we can see that it is negative, so looking at the answers we can mark answer $C$ $C$ . The value is about $- 0.99$ $-0.99$

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Compute the exact value of $\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$ without a calcuator?

$\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$

1 Answer

Explanation:

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Compute the exact value of tan220∘−sin220∘tan220∘sin220∘{tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ} without a calcuator?

tan220∘−sin220∘tan220∘sin220∘{tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}

1 Answer

Explanation:

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Compute the exact value of $\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$ without a calcuator?

$\frac{{tan 220}^{\circ} - {sin 220}^{\circ}}{{tan 220}^{\circ} {sin 220}^{\circ}}$ ${tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}$