Sin30^2+cos60^2+sin30cos60=3/4 Sin20^2+cos50^2+sin20cos50=3/4 Sin15^2+cos45^2+sin15cos45=3/4 Analyze the common characteristics of the above formulas, write the equation that can reflect the general law, and prove it

Sin30^2+cos60^2+sin30cos60=3/4 Sin20^2+cos50^2+sin20cos50=3/4 Sin15^2+cos45^2+sin15cos45=3/4 Analyze the common characteristics of the above formulas, write the equation that can reflect the general law, and prove it

The equation of general law: [sin α] ^ 2 + [cos (α + 30)] ^ 2 + sin α cos (α + 30) = 3 / 4
It is proved that the left end = [sin α] ^ 2 + [√ 3 / 2cos α - 1 / 2Sin α] ^ 2 + sin α [√ 3 / 2cos α - 1 / 2Sin α] = [sin α] ^ 2 + 3 / 4 [cos α] ^ 2 + 1 / 4 [sin α] ^ 2-1 / 2 [sin α] ^ 2 = 3 / 4 [sin α] ^ 2 + 3 / 4 [cos α] ^ 2 = 3 / 4

（cos40）＋（sin40）=?
The square of cos40.
The square of sin40

Root sign 2Sin (40 ° + 45 °) = root sign 2sin85 °
The sum of squares equals one

Tan 70 degrees * sin 40 degrees - cos 40 degrees

Tan 70 degrees * sin 40 degrees - cos 40 degrees
=cot20*sin40-cos40
=cos20/sin20*(2sin20cos20)-cos40
=2cos^2(20)-cos40
=2cos^2(20)-(2cos^2(20)-1)
=1

How to use algebra to compare numbers
For example, 1: - 1 / 2___ -2 / 3, or a = 2007 / 2008, B = 2008 / 2009, try to compare the size of a and B without small fraction

Commercial Law
Compare 1 / 2 and 2 / 3 first
1/2÷2/3=1/3