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How does this? sin^2 20 + sin^2 70 =   20 and 70 are in grade

Guest Jun 8, 2015

Best Answer 

 #2
avatar+94105 
+10

Draw a right angled triangles with angles 20 and 70 degrees.  

Convince yourself that sin70 = cos 20

 

Now 

$$\\sin^2 20 + sin^2 70 \\\\
=sin^2 20 + cos^2 20 \\\\
=1\\\\\\
remember\; the\; identity\\\\
\boxed{sin^2 \theta + cos^2 \theta=1}$$

Melody  Jun 9, 2015
 #1
avatar+14536 
+5

$${\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{20}}^\circ\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}\left({\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}^{\,{\mathtt{2}}}\right) = {\mathtt{1}}$$

$${\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{20}}^\circ\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}^{\,{\mathtt{2}}} = {\mathtt{1.000\: \!000\: \!000\: \!000\: \!398\: \!8}}$$

radix  Jun 8, 2015
 #2
avatar+94105 
+10
Best Answer

Draw a right angled triangles with angles 20 and 70 degrees.  

Convince yourself that sin70 = cos 20

 

Now 

$$\\sin^2 20 + sin^2 70 \\\\
=sin^2 20 + cos^2 20 \\\\
=1\\\\\\
remember\; the\; identity\\\\
\boxed{sin^2 \theta + cos^2 \theta=1}$$

Melody  Jun 9, 2015

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