Question

If sin a + cosec a = 2, find the value of sin" & + cosec" a.​

Answer 1

Given,

sin A + cosec A = 2.................[1]

To find: sin²A + cosec²A

Squaring [1] on both sides,

(sin A + cosec A)² = 2²

→sin²A + cosec²A + 2sinAcosecA=4

→sin²A + cosec²A = 4-2sinAcosecA

→sin²A + cosec²A =4-2 [since, sin A = 1/cosec A]

→sin²A + cosec²A = 2