Question

14sin(t)cos(t)=2cos(t).

a) sin(t)=1/7
b) sin(t)=1/2
c) sin(t)=7
d) sin(t)=2cos(t)

Answer 1

The equation 14sin(t)cos(t)=2cos(t) simplifies to 14sin(t) = 2 when factoring out and canceling cos(t). Dividing both sides by 14 gives sin(t) = 1/7.

Step-by-step explanation:

To solve the equation 14sin(t)cos(t)=2cos(t), we first look for common factors. We notice that cos(t) is a common factor on both sides of the equation, so we can simplify by dividing both sides by cos(t), assuming that cos(t) is not equal to zero. Doing so, we get:

14sin(t) = 2

Next, we divide both sides by 14 to solve for sin(t):

sin(t) = 2/14

sin(t) = 1/7

Thus, the correct answer to the question is a) sin(t)=1/7.