Chapter 7: Q. 1 (page 500)

Find the exact value of the expression:
$\sin 195 ° \cdot \cos 75 °$

Short Answer

Expert verified

The exact value is $\frac{1}{2} [\frac{\sqrt{3}}{2} - 1]$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\sin 195 ° \cdot \cos 75 °$

We know localid="1646458669499" role="math" $\sin a \cdot \sin b = \frac{1}{2} [\sin (a + b) + \sin (a - b)]$ .

Using the formula, we get,

$\sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [\sin (195 ° + 75 °) + \sin (195 ° - 75 °)]$

Step 2. Simplify the equation.

Continuing the above equation,

$\sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [\sin (270 °) + \sin (120 °)] \sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [- 1 + \frac{\sqrt{3}}{2}] \sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [\frac{\sqrt{3}}{2} - 1]$

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Find the exact value of the expression:
$\sin 195 ° \cdot \cos 75 °$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

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Find the exact value of the expression:sin195°·cos75°

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

One App. One Place for Learning.

Most popular questions from this chapter

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Find the exact value of the expression:
$\sin 195 ° \cdot \cos 75 °$