Question

simplyfy cos45+sin30​

Answer 1

Question:

Simply cos45+sin30

Solution:

We know that,

$\sf{cos45 = \frac{1}{ \sqrt{2} } } \\ \\ \sf{and \: sin30 = \frac{1}{2} }$

Now,

$\sf{sin30 + cos45} \\ \\ \sf{ = \frac{1}{2} + \frac{1}{ \sqrt{2} } } \\ \\ = \underline{\boxed{\sf{ \frac{2 + \sqrt{2} }{2 \sqrt{2} } }}}$

Denominator should not contain any radical sign

On rationalizing the denominator,

$\frac{2 + \sqrt{2} }{2 \sqrt{2} } \times \frac{2 \sqrt{2} }{2 \sqrt{2} } \\ \\ = \underline{\boxed{ \sf{ \frac{4( \sqrt{2} + 1)}{8} }}}$

It can be further written as (√2+1)/2

Trigonometric values have been taken from the trigonometric table