Question

the value of cos 105°
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Answer 1

Given: cos 105°

We have to find the value of cos 105°.

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★ cos 105° can be written as cos(60 + 45)

Here, we use

• cos(A + B) = cosA . cosB - sinA . sinB

.

Applying the formula

$\tt\longrightarrow{cos(60 + 45)}$

$\tt\longrightarrow{cos60^{\circ} . cos45^{\circ} - sin60^{\circ} . sin45^{\circ}}$

.

Values are :-

.

• $\bf{cos60^{\circ} = \dfrac{1}{2}}$

.

• $\bf{cos45^{\circ} = \dfrac{1}{\sqrt{2}}}$

.

• $\bf{sin60^{\circ} = \dfrac{\sqrt{3}}{2}}$

.

• $\bf{sin45^{\circ} = \dfrac{1}{\sqrt{2}}}$

.

Putting the values

$\tt\longrightarrow{\dfrac{1}{2} \times \dfrac{1}{\sqrt{2}} - \dfrac{\sqrt{3}}{2} \times \dfrac{1}{\sqrt{2}}}$

.

$\tt\longrightarrow{\dfrac{1}{2 \sqrt{2}} - \dfrac{\sqrt{3}}{2 \sqrt{2}}}$

.

$\tt\longrightarrow{\dfrac{1 - \sqrt{3}}{2 \sqrt{2}}}$

.

Hence,

• Value of cos 105° is $\bf{\dfrac{1 - \sqrt{3}}{2 \sqrt{2}}}$.