SinA+cosecA=2;

Find the value of sin²A + cosec²A.

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Solution

Given

sinA + cosecA = 2

Squaring on both sides

(sinA + cosecA)² = 2²

sin^2A + cosec^2A + 2 sinA cosecA = 4

sin^2A + cosec^2A = 4 - 2 sinAcosecA

WKT cosec A = 1/sinA

sin^2A + cosec^2A = 4 -2

∴ sin^2A + cosec^2A = 2

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