Chapter 7: Q. 3 (page 500)

find the exact value of the expression
sin 285 $°$ sin 75 $°$

Short Answer

Expert verified

$\sin 285 ° \sin 75 ° = - 0.9330127019$

Step by step solution

Step 1. Rewriting the expression

sin(270 $°$ +x)= $-$ cos(x )

sin285 $°$ =sin(270 $°$ +15 $°$ ) = $- \cos (15 °)$

Given expression becomes

sin 285 $°$ sin 75 $°$ = $-$ cos15 $°$ sin75 $°$

Step 2. Calculations

cos(90 $°$ $-$ x)=sin(x)

so, sin75 $°$ =cos(90 $° -$ 75 $°$ )=cos15 $°$

So now the expression becomes

$-$ cos15 $°$ cos15 $°$ = $- \cos^{2} (15 °)$

We know that

cos(2x)= $2 \cos^{2} x - 1$

role="math" localid="1646416466227" $\cos^{2} x = \frac{1 + \cos 2 x}{2} - \cos^{2} 15 ° = \frac{1 + \cos 30 °}{2} = \frac{1 + \frac{\sqrt{3}}{2}}{2} = - 0.9330127019$

Therefore,role="math" localid="1646416523469" $\sin 285 ° \sin 75 ° = - 0.9330127019$

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find the exact value of the expression
sin 285 $°$ sin 75 $°$

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. Calculations

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find the exact value of the expression sin 285°sin 75°

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Geometry

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

find the exact value of the expression
sin 285 $°$ sin 75 $°$