Question

Find the values of the following:
(i)
(cos 0° + sin 45° + sin 30°)(sin 90° - cos 45º + cos 60°)​

Answer 1

Step-by-step explanation:

(cos0° + sin45° + sin30°)(sin90° - cos45° + cos60°)

$(1 + \frac{1}{ \sqrt{2} } + \frac{1}{2} )(1 - \frac{1}{ \sqrt{2} } + \frac{1}{2} ) \\ \\ = (\frac{3}{2} + \frac{1}{ \sqrt{2} } )( \frac{3}{2} - \frac{1}{ \sqrt{2} } ) \\ \\ = {( \frac{3}{2} )}^{2} - {( \frac{1}{ \sqrt{2} }) }^{2} \\ \\ = \frac{9}{4} - \frac{1}{2} \\ \\ = \frac{9 - 2}{4} \\ \\ = \frac{7}{4} \\ = 1 \frac{3}{4}$

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