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