Chapter 6: Q. 8 (page 436)

find the exact value of the expression
$\cos (- \frac{5 π}{4}) - \cos (\frac{3 π}{4})$

Short Answer

Expert verified

Value of the expression is 0

Step by step solution

Step 1. Given information

$\cos (- \frac{5 π}{4}) - \cos (\frac{3 π}{4})$

Step 2. Rewriting the expression

As cos is a even function so, cos(x)=cos(-x)

So given expression can be written as $\cos (\frac{5 π}{4}) - \cos (\frac{3 π}{4})$

Step 3. Calculations

$W e k n o w t h a t \cos (π + x) = - \cos (x) \cos (π - x) = - \cos (x) S o, \cos (\frac{5 π}{4}) = \cos (π + \frac{π}{4}) = - \cos (\frac{π}{4}) \cos (\frac{53 π}{4}) = \cos (π - \frac{π}{4}) = - \cos (\frac{π}{4}) So, \cos (\frac{5 π}{4}) - \cos (\frac{53 π}{4}) = 0$

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find the exact value of the expression
$\cos (- \frac{5 π}{4}) - \cos (\frac{3 π}{4})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewriting the expression

Step 3. Calculations

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find the exact value of the expressioncos-5π4-cos3π4

Short Answer

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Step 3. Calculations

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find the exact value of the expression
$\cos (- \frac{5 π}{4}) - \cos (\frac{3 π}{4})$