Question

Дано:sina+cosa=p найти:sina*cosa

Answer 1

(sin(a)+cos(a))^2=p^2

(sin(a)+cos(a))^2=sin(a)^2+ 2sin(a)*cos(a)+cos(a)^2= 1+2sin(a)*cos(a)

1+2sin(a)*cos(a)=p^2
sin(a)*cos(a)=(p^2 + 1)/2

Answer 2

To find the value of sin(a) * cos(a) given that sin(a) + cos(a) = p, we can use trigonometric identities to express sin(a) * cos(a) in terms of p.

Step 1: Square both sides of the equation sin(a) + cos(a) = p: (sin(a) + cos(a))^2 = p^2

Step 2: Expand the left side of the equation: sin^2(a) + 2*sin(a)*cos(a) + cos^2(a) = p^2

Step 3: Use the Pythagorean identity sin^2(a) + cos^2(a) = 1: 1 + 2*sin(a)*cos(a) = p^2

Step 4: Rearrange the equation to solve for sin(a)cos(a): 2sin(a)*cos(a) = p^2 - 1

Step 5: Finally, divide both sides by 2 to obtain the value of sin(a) * cos(a): sin(a) * cos(a) = (p^2 - 1) / 2

So, the value of sin(a) * cos(a) is (p^2 - 1) / 2.