Question

Sinx+cosx=1.4 найти sin2x

Answer 1

Ответ:

sinx+cosx=1.4

(sinx+cosx)^2=1.4^2

sin^2x+cos^2x+2sinxcosx=1.96

1+2sinxcosx=1.96

2sinxcosx=0.96

sin2x=0.96

Answer 2

To find the value of sin(2x), we can use the trigonometric identity:

sin(2x) = 2sin(x)cos(x)

First, let's rearrange the given equation sin(x) + cos(x) = 1.4 to solve for sin(x):

sin(x) = 1.4 - cos(x)

Now, substitute this value of sin(x) into the formula for sin(2x):

sin(2x) = 2sin(x)cos(x) = 2(1.4 - cos(x))cos(x) = 2.8cos(x) - 2cos^2(x)

We still need the value of cos(x) to compute sin(2x). Unfortunately, the equation sin(x) + cos(x) = 1.4 is not enough to determine the exact values of sin(x) and cos(x) individually. We would need another equation or additional information to solve for cos(x) and, consequently, find the value of sin(2x).