prove the 14th one.
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(cosecA + sinA)(cosecA-sinA) = cot²A + cos²A
Putting the formula (a+b)(a-b) = a²-b², we get,
cosec²A - sin²A = cot²A + cos²A
1+cot²A-(1-cos²A) = cot²A + cos²A
1+cot²A-1+cos²A = cot²A + cos²A
cot²A + cos²A = cot²A + cos²A
LHS = RHS Proved
Putting the formula (a+b)(a-b) = a²-b², we get,
cosec²A - sin²A = cot²A + cos²A
1+cot²A-(1-cos²A) = cot²A + cos²A
1+cot²A-1+cos²A = cot²A + cos²A
cot²A + cos²A = cot²A + cos²A
LHS = RHS Proved
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see attachment. ..I hope it will help u.
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