Question

(1-sin45+sin30) (1+cos45+cos60)=7/4

Answer 1

(1- sin45 + sin 30 )(1+ cos45 + cos60)

( 1- 1√2 + 1/2 ) ( 1+ 1/√2 + 1/2)

( 1/2 - 1/√2) ( 3/2 + 1/√2)

(1-√2 / 2)(3+√2/2)

(1-√2)(3+√2)/4

7/4

Answer 2

Answer:

The proof has been shown below.

Step-by-step explanation:

We have been given the expression in left side

(1-sin45+sin30) (1+cos45+cos60)

We have the values,

sin45 = 1/√2

sin30 = 1/2

cos45 = 1/√2

cos 60 = 1/2

On substituting these values, we get

$\left ( 1-\frac{1}{\sqrt2}+\frac{1}{2} \right )\left ( 1+\frac{1}{\sqrt2}+\frac{1}{2} \right )\\\\\\(\frac{2-\sqrt2+1}{2})(\frac{2+\sqrt2+1}{2})\\\\\\\frac{3-\sqrt2}{2}\times\frac{3+\sqrt2}{2}\\\\\\\frac{(3-\sqrt2)(3+\sqrt2)}{4}\\\text{Using the formula }a^2-b^2=(a+b)(a-b)\\\\\frac{(3)^2-(\sqrt2)^2}{2}\\\\\frac{9-2}{4}\\\\\frac{7}{4}$