Question

14
Prove that
(sino + coseco)²+(coso+seco)²=7 tan²o+cot²o
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Answer 1

(sino + coseco)²+(coso + seco)²=7 + tan²o + cot²o

Take LHS:

» sin²o + cosec²o + 2 + cosec²o + sec²o + 2 [ •.• sinx.cosecx = 1, secs.cosx = 1]

» 1 + 1 + cot²o + 4 + 1 + tan²o [•.• sin²x + cos²x = 1, cosec²x = 1 + cot²x, sec²x = 1 + tan²x]

» 7 + tan²o + cot²o

Hence Proved.