Question

Еслиsina + cosa=mто sina×cosa=?​

Answer 1

$\sin a + \cos a=m$

Возведем в квадрат:

$(\sin a + \cos a)^2=m^2$

$\sin^2a+2\sin a\cos a+ \cos^2a=m^2$

$(\sin^2a+ \cos^2a)+2\sin a\cos a=m^2$

Воспользуемся основным тригонометрическим тождеством:

$1+2\sin a\cos a=m^2$

$2\sin a\cos a=m^2-1$

Искомое произведение:

$\sin a\cos a=\dfrac{m^2-1}{2}$

Answer 2

To solve this problem, we'll need to use trigonometric identities and equations.

Given: sina + cosa = m

We'll square both sides of the equation to eliminate the square roots:

(sina + cosa)^2 = m^2

Expanding the left side using the binomial formula, we get:

sina^2 + 2sina*cosa + cosa^2 = m^2

Now, we'll use the trigonometric identity sina^2 + cosa^2 = 1:

1 + 2sina*cosa = m^2

Rearranging the equation, we have:

2sina*cosa = m^2 - 1

Finally, dividing both sides by 2, we find:

sina*cosa = (m^2 - 1) / 2

Therefore, sina*cosa is equal to (m^2 - 1) / 2.