Question

1.1 If A = 40° and B = 25°, calculate, correct to ONE decimal place, each of the following: 1.1.1 cosec2 B 1.1.2 tan (A - B)​

Answer 1

1.1.1 To find cosec2 B, we first need to find the value of the sine of B:

sin B = sin 25° ≈ 0.4226

Then we can use the formula:

cosec2 B = 1/sin2 B

cosec2 25° ≈ 4.2904

Rounded to one decimal place, cosec2 25° is approximately 4.3.

1.1.2 To find tan (A - B), we first need to find the values of the tangent of A and B:

tan A = tan 40° ≈ 0.8391
tan B = tan 25° ≈ 0.4663

Then, we can use the formula:

tan (A - B) = (tan A - tan B) / (1 + tan A tan B)

tan (40° - 25°) = (0.8391 - 0.4663) / (1 + (0.8391)(0.4663))

tan 15° ≈ 0.268

Rounded to one decimal place, tan (40° - 25°) is approximately 0.3.