Question

If sin + cosec=2 find the value of cos^2-cot^2

Answer 1

Solution :

Given sinA + cosecA = 2---(1)

Do the square both sides

of equation (1) , we get

(sinA + cosecA)² = 2²

=> sin²A + cosec²A +2sinAcosecA = 4

=> 1 - cos²A + 1 + cot²A + 2 = 4

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[ Since , i )sin²A = 1 - cos²A

ii ) cosec²A = 1 + cot²A

iii ) sinAcosecA = 1

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=> 4 - 4 = cos²A - cot²A

=> 0 = cos²A - cot²A

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