Question

Sin²a + sin a - 1 + cos²a=sin a​

Answer 1

Согласно основному тригонометрическому тождеству:

${sin}^{2} x + {cos}^{2} x = 1$

Отсюда:

${sin}^{2} a + sin \: a - 1 + {cos}^{2} a = sin \: a \\ 1 + sin \: a - 1 = sin \: a \\ sin \: a = sin \: a$

Это значит, что данное равенство выполняется для любого угла а.

Answer 2

Let's simplify the given equation step by step:

Starting with the equation: sin²a + sin a - 1 + cos²a = sin a

Since sin²a + cos²a = 1 (using the Pythagorean identity), we can substitute this into the equation: 1 + sin a - 1 + cos²a = sin a

The two "1" terms cancel each other out: sin a + cos²a = sin a

Subtracting sin a from both sides: cos²a = 0

Taking the square root of both sides: cos a = 0

Now, we need to find the values of "a" where the cosine function equals zero. The cosine function is equal to zero at two specific angles: 90 degrees and 270 degrees (π/2 and 3π/2 in radians).

So the possible solutions for "a" are: a = 90 degrees + 360 degrees * n, where n is an integer a = 270 degrees + 360 degrees * n, where n is an integer

In radians: a = π/2 + 2πn, where n is an integer a = 3π/2 + 2πn, where n is an integer

These are the values of "a" that satisfy the given equation.