That is, the sum of squares of sine and cosine at the same angle is equal to 1.

The proof is as follows: Let an inner angle of an α-right triangle, the hypotenuse is C, the opposite side is A, and the adjacent side is B, then there is:

sinα=a/c

cosα=b/c

So there are:

Sin? a+cos？ a

=(a/c)^2+(b/c)^2

= (A 2+B 2)/C 2 Because there is: C 2 = A 2+B 2 (Pythagorean Theorem) in a right triangle.

=c^2/c^2

= 1

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Because a = x 4+2x+6 in this problem accords with the sum of squares of sine and cosine of the same angle in this formula, the result is 1.

hope this helps