Question

Cosec (A-B) =
secA secB÷
tanA - tanB then cosec15°=?​

Answer 1

Explaining trigonometry:

Trigonometry is the study of angles and the relation between angles and its ratios. It deals with the property of triangles in terms of ratios of angles and its sides.

Let us get to know some trigonometric relations and identities as follows,

• sinA = cos(90° - A)

• cosA = sin(90° - A)

• sinA / cosA = tanA

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

• sin(A + B) = sinA cosB + cosA sinB

and many more . . .

Solution:

Given formula,

cosec(A - B) = secA secB / (tanA - tanB)

Here, 15° = 45° - 30°

Taking cosec in both sides, we get

cosec15° = cosec(45° - 30°)

= sec45° sec30° / (tan45° - tan30°)

= (√2 * 2/√3) / (1 - 1/√3)

= (2√2 / √3) / {(√3 - 1) / √3}

= 2√2 / (√3 - 1)

Hence, cosec15° = 2√2 / (√3 - 1)