Question

(cos 0+sin 45+sin 30)(sin 90-cos 45+cos 60)

Answer 1

Please see attachment.

7/4 is the final answer.

Hope it helps.

Answer 2

Answer:

$\frac{7}{4}$

Explanation:

______________________

We know the values of

i) cos0° = 1

ii) sin45° = $\frac{1}{\sqrt{2}}$

iii) sin30° = $\frac{1}{2}$

iv) sin90° = 0

v) cos45° = $\frac{1}{\sqrt{2}}$

vi ) cos60° = $\frac{1}{2}$

_____________________

Now,

The value of

(cos 0+sin 45+sin 30)(sin 90-cos 45+cos 60)

= $\left(1+\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(1-\frac{1}{\sqrt{2}}+\frac{1}{2}\right)$

= $\left(\frac{3}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{3}{2}-\frac{1}{\sqrt{2}}\right)$

= $\left(\frac{3}{2}\right)^{2}-\left(\frac{1}{\sqrt{2}}\right)^{2}$

/* By algebraic identity

(a-b)(a+b) = a²-b² */

= $\left( \frac{9}{4}-\frac{1}{2}\right)$

= $\frac{9-2}{4}$

= $\frac{7}{4}$

••••