Question

sin45°cos45°-sin30°=?

Answer 1

⭐ $sin45 = \frac{ 1 }{2}$

⭐ $cos45 = \frac{1}{2}$

⭐ $sin30 = \frac{1}{ \sqrt{2} }$

$\:put\:all\:these\:values\:in\:the\:given\: equation$

⟹ $\dfrac{1}{2}$ ×$\dfrac{1}{2}$ - $\dfrac{1}{√2}$

⟹ $\dfrac{1}{4}$ - $\dfrac{1}{√2}$

⟹ $\dfrac{√2 - 4}{4√2}$

Rationalising The denominator

⟶ $\dfrac{√2 - 4}{4√2}$

⟶ $\dfrac{√2 - 4}{4√2}$ × $\dfrac{4√2}{4√2}$

⟶ $\dfrac{8 - 16√2}{32}$

Hope it helps u

Answer 2

Answer:

✈️${\huge{\pink{\underline{\underline{Question}}}}}$✈️

sin45°cos45°-sin30°=?

✈️${\huge{\pink{\underline{\underline{Values}}}}}$✈️

• ✍️$sin\ 45°=\frac{1}{2}$✍️
• ✍️$cos\ 45°=\frac{1}{2}$✍️
• ✍️$sin\ 30°=\frac{1}{\sqrt{2}}$✍️

✈️${\huge{\pink{\underline{\underline{Solution}}}}}$✈️

Put the values into given question;

$sin\ 45°\ cos\ 45° -sin\ 30°$

$=\frac{1}{2}×\frac{1}{2}-\frac{1}{\sqrt{2}}$

$=\frac{1×1}{2×2}-\frac{1}{\sqrt{2}}$

$=\frac{1}{4}-\frac{1}{\sqrt{2}}$

$=\frac{\sqrt{2}-4}{4\sqrt{2}}$

Now,Rationalise the term;

$=\frac{\sqrt{2}-4}{4\sqrt{2}}×\frac{4\sqrt{2}}{4\sqrt{2}}$

$=>\frac{4\sqrt{2}×(\sqrt{2}-4)}{{4\sqrt{2}}^{2}}$

$=>\frac{8-16\sqrt{2}}{32}$