Question

sin45degree-sin30degree/cos45degree+cos60degree
​

Answer 1

Answer:

=sin45degree-sin30degree/cos45degree+cos60degree

=0.7-0.5/0.7+0.5

=0.2/1.2

=0.16667

Answer 2

Answer:

3 - 2√2

Step-by-step explanation:

$sin45^0=cos45^0=\frac{1}{\sqrt{2}} \\\\ sin30^0=cos60^0=\frac{1}{2} \\\\ \implies\frac{sin45^0-sin30^0}{cos45^0+cos60^0} \\\\ \implies \frac{\frac{1}{\sqrt{2}}-\frac{1}{2}}{\frac{1}{\sqrt{2}}+\frac{1}{2}}\\\\ \implies \frac{\frac{2-\sqrt{2}}{2\sqrt{2}} }{\frac{2+\sqrt{2}}{2\sqrt{2}}}\\\\ \implies \frac{2-\sqrt{2}}{2+\sqrt{2}} \\\\ rationalising \ factor=2-\sqrt{2}\\\\=>\frac{2-\sqrt{2}}{2+\sqrt{2}} \times \frac{2-\sqrt{2}}{2-\sqrt{2}} \\\\ \implies \frac{(2-\sqrt{2})(2-\sqrt{2})}{(2+\sqrt{2})(2-\sqrt{2})}$

$\implies \frac{(2-\sqrt{2})^{2} }{2^2-\sqrt{2}^2} \\\\ \implies \frac{2^2+\sqrt{2}^2-2(2)(\sqrt{2})}{4-2} \\\\ \implies \frac{4+2-4\sqrt{2}}{2} \\\\ \implies \frac{6-4\sqrt{2}}{2} \\\\ \implies 3-2\sqrt{2}$

______________________

Formula used:

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²