4.3 Without using a calculator, determine the value of:

Ask by Davies Clarke. in South Africa

Mar 19,2025

Question

4.3 Without using a calculator, determine the value of: $$ \sin ^{2} 45^{\circ}-\cos 60^{\circ}+	an 10^{\circ} \cdot \cot 10^{\circ} $$

UpStudy AI · Accepted Answer

1. First, calculate $$ \sin 45^\circ $$:
   $$
   \sin 45^\circ = \frac{\sqrt{2}}{2}
   $$
   Then, square the result:
   $$
   \sin^2 45^\circ = \left(\frac{\sqrt{2}}{2}\right)^2 = \frac{1}{2}
   $$

2. Next, evaluate $$ \cos 60^\circ $$:
   $$
   \cos 60^\circ = \frac{1}{2}
   $$

3. Now, consider $$ \tan 10^\circ \cdot \cot 10^\circ $$. Since $$ \cot 10^\circ = \frac{1}{\tan 10^\circ} $$:
   $$
   \tan 10^\circ \cdot \cot 10^\circ = \tan 10^\circ \cdot \frac{1}{\tan 10^\circ} = 1
   $$

4. Combine the results:
   $$
   \sin^2 45^\circ - \cos 60^\circ + \tan 10^\circ \cdot \cot 10^\circ = \frac{1}{2} - \frac{1}{2} + 1 = 1
   $$

Thus, the value of the expression is $$ 1 $$.
The value of the expression $$ \sin ^{2} 45^{\circ}-\cos 60^{\circ}+\tan 10^{\circ} \cdot \cot 10^{\circ} $$ is $$ 1 $$.

4.3 Without using a calculator, determine the value of:

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