Question

sin square 45 degree + cos square 45 degree is equal to how

Answer 1

$\textbf{Standard trigonometric table:}$

$\left\begin{array}{|c|c|c|c|c|c|}\cline{1-6}&0^{\circ}&30^{\circ}&45^{\circ}&60^{\circ}&90^{\circ}\\\cline{1-6}\bf\,sin\theta&0&\frac{1}{2}&\frac{1}{\sqrt2}&\frac{\sqrt3}{2}&1\\\cline{1-6}\bf\,cos\theta&1&\frac{\sqrt3}{2}&\frac{1}{\sqrt2}&\frac{1}{2}&0\\\cline{1-6}\bf\,tan\theta&0&\frac{1}{\sqrt3}&1&\sqrt3&\infty\\\cline{1-6}\end{array}\right$

$\text{From the table, it is clear that}$

$sin\,45^{\circ}=\frac{1}{\sqrt2}$

$cos\,45^{\circ}=\frac{1}{\sqrt2}$

$\text{Now}$

$sin^245^{\circ}+cos^245^{\circ}$

$=(\frac{1}{\sqrt2})^2+(\frac{1}{\sqrt2})^2$

$=\frac{1}{2}+(\frac{1}{2}$

$=1$

$\therefore\boxed{\bf\,sin^245^{\circ}+cos^245^{\circ}=1}$

Find more:

Cos²10+Cos²20+Cos²30+Cos²40+Cos²50+Cos²60+Cos²70+Cos²80+Cos²90.

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Answer 2

The value of sin square 45 degree + cos square 45 is equal to 1.

• According to the sine curve, the value of sine ranges from -1 to +1.
• And the value of sin 45 degree is 1 /  $\sqrt{2}$.
• Similarly, the value of cosine ranges from -1 to +1 which is evident from the cosine curve.

• So, the value of cosine 45 degree is 1 / $\sqrt{2}$.

• So, on squaring and adding we get,

          sine square 45 + cos square 45 = 1/2 +1/2 =1 .