Question

Evaluate (sin30 + sin45)(cos60-cos45)

Answer 1

Answer:

-1/4

Step-by-step explanation:

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Answer 2

SOLUTION

TO DETERMINE

The value of

(sin 30° + sin 45°)(cos 60° - cos 45° )

EVALUATION

Here the given expression is

(sin 30° + sin 45°)(cos 60° - cos 45° )

We simplify it as below

(sin 30° + sin 45°)(cos 60° - cos 45° )

$\displaystyle \sf{ = \bigg( \frac{1}{2} + \frac{1}{ \sqrt{2} } \bigg)\bigg( \frac{1}{2} - \frac{1}{ \sqrt{2} } \bigg)}$

$\displaystyle \sf{ = {\bigg( \frac{1}{2} \bigg)}^{2} -{ \bigg( \frac{1}{ \sqrt{2} } \bigg)}^{2} }$

$\displaystyle \sf{ = \frac{1}{4} - \frac{1}{2} }$

$\displaystyle \sf{ = \frac{1 - 2}{4} }$

$\displaystyle \sf{ = - \frac{1}{4} }$

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