Question

value of( cos 0 degree + sin 45 degree+ sin30degree)(sin 90degree×cos45 degree+cos 60 degree

Answer 1

$( \cos(0) + \sin(45) + \sin(30) )( \sin(90) \times \cos(45) + \cos(60))$
$(1 + \frac{1}{ \sqrt{2} } + \frac{1}{2} )( \: \frac{1}{ \sqrt{2}} + \frac{1}{2} )$
$( \frac{3 \sqrt{2} + 2 }{2 \sqrt{2} } )( \frac{2 + \sqrt{2} }{2 \sqrt{2} } )$
$\frac{6 \sqrt{2} +4 + 6 + 2 \sqrt{2} }{8}$
$\frac{10 + 8 \sqrt{2} }{8}$
$\frac{5 + 4 \sqrt{2} }{4}$

Answer 2

Let's divide the problem into first half and 2nd half then we'll multiply them so that it's easy.
Let's do the first one,
$= \cos(0) + \sin(45) + \sin(30) \\ = 1 + \frac{1}{ \sqrt{2} } + \frac{1}{2} \\ = \frac{2}{2} + \frac{1}{2} + \frac{ \sqrt{2} }{2} \\ = \frac{3 + \sqrt{2} }{2}$
Now let's take part 2,
$= \sin(90) + \times \cos(45) + \cos(60) \\ = 1 \times \frac{1}{ \sqrt{2} } + \frac{1}{2} \\ = \frac{ \sqrt{2} + 1 }{2}$
Multiply the above ones to get the answer,
$= \frac{ \sqrt{2} + 1}{2} \times \frac{3 + \sqrt{2} }{2} \\ = \frac{3 \sqrt{2} + \sqrt{2} + 5 }{4} \\ = \sqrt{2} + \frac{5}{4}$
Or
\frac{4√2 +5}{4}
Therefore, the answer is √2 +5/4