For 0 <or equal B <or equal 2 pi

determine all solutions of

sinB + cos B = SinBcosB

find the area circle with a 7inches radius.use22/7.

To determine all solutions of the equation sin(B) + cos(B) = sin(B)cos(B), we will manipulate the equation to solve for B.

Step 1: Rearrange the equation to isolate the trigonometric terms.
sin(B) + cos(B) = sin(B)cos(B)
sin(B) + cos(B) - sin(B)cos(B) = 0

Step 2: Factor out the common sin(B) term.
sin(B)[1 - cos(B)] + cos(B) = 0

Step 3: Apply the zero product property and set each factor equal to zero.
sin(B) = 0 or 1 - cos(B) = 0

Step 4: Solve each equation separately.

Equation 1: sin(B) = 0
B = 0°, 180°

Equation 2: 1 - cos(B) = 0
cos(B) = 1
B = 0°

Therefore, the solutions for 0 ≤ B ≤ 2π are B = 0°, 180°.

Moving on to the second question, to find the area of a circle with a 7-inch radius, we can use the formula A = πr², where A represents the area and r represents the radius.

Step 1: Plug in the given values.
A = π(7)²

Step 2: Calculate the square of the radius.
A = π(49)

Step 3: Simplify the expression.
A = 49π

Step 4: Approximate the value of π as 22/7.
A ≈ 49 * (22/7)
A ≈ 154

Therefore, the area of a circle with a 7-inch radius is approximately 154 square inches.