Question

(sin a - cosa)² + (sin a + cosa)² = ​

Answer 1

Ответ:

vot, otvet na listochke (sprava trigonometricheskaya formula)

Answer 2

To simplify the expression (sin a - cos a)² + (sin a + cos a)², let's expand and simplify each term separately:

Expanding the first term: (sin a - cos a)² = sin² a - 2 sin a cos a + cos² a

Expanding the second term: (sin a + cos a)² = sin² a + 2 sin a cos a + cos² a

Adding the two expanded terms together: (sin a - cos a)² + (sin a + cos a)² = (sin² a - 2 sin a cos a + cos² a) + (sin² a + 2 sin a cos a + cos² a)

Combining like terms: (sin a - cos a)² + (sin a + cos a)² = sin² a + sin² a + cos² a + cos² a - 2 sin a cos a + 2 sin a cos a

Simplifying further: (sin a - cos a)² + (sin a + cos a)² = 2 sin² a + 2 cos² a

Since sin² a + cos² a = 1 (a fundamental trigonometric identity), we can substitute this in: (sin a - cos a)² + (sin a + cos a)² = 2(1) = 2

Therefore, (sin a - cos a)² + (sin a + cos a)² simplifies to 2.