Question

(cos 0 + sin 45+sin 30)(sin90-cos45+cos60)​

Answer 1

Answer:

$\large\boxed{\sf{\dfrac{7}{4}}}$

Step-by-step explanation:

We have to find the value of,

$( \cos0 + \sin45 + \sin30 ) ( \sin90 - \cos45 + \cos60)$

Now, We know the values of,

• $\cos(0) = 1$

• $\cos(45) = \frac{1}{ \sqrt{2} }$

• $\cos(60) = \frac{1}{2}$

• $\sin(30) = \frac{1}{2}$

• $\sin(45) = \frac{1}{ \sqrt{2} }$

• $\sin(90) = 1$

Substituting the values, We get,

$= (1 + \dfrac{1}{ \sqrt{2} } + \dfrac{1}{2} )(1 - \dfrac{1}{ \sqrt{2} } + \dfrac{1}{2} ) \\ \\ = ( \dfrac{3}{2} + \dfrac{1}{ \sqrt{2} } )( \dfrac{3}{2} - \dfrac{1}{ \sqrt{2} } ) \\ \\ = {( \dfrac{3}{2}) }^{2} - {( \dfrac{1}{ \sqrt{2} }) }^{2} \\ \\ = \dfrac{9}{4} - \dfrac{1}{2} \\ \\ = \dfrac{18 - 4}{8} \\ \\ = \dfrac{14}{8} \\ \\ = \dfrac{7}{4}$