Prove that (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Take left hand side of the given equation:
LHS = (sin A + cosec A)2 + (cos A + sec A)2
Expanding the squares by formula: (a + b)2 = a2 + b2 + 2ab= sin2 A + cosec2 A + 2 sin A cosec A + cos2 A + sec2 A + 2 cos A sec A
Rearranging the terms, we get,= (sin2 A + cos2 A) + 2 sin A cosec A + 2 cos A sec A + cosec2 A + sec2 A
we know that,
= 
= 
= 5 + 1/(sin2 A cos2 A) …(i)
Now, take right hand side of the equation:
RHS = 7 + tan2 A + cot2 A
= 
= 
= 
= 
= 5 + 1/(sin2 A cos2 A) …(ii)
From equation (i) & (ii),
LHS = RHS
Hence, proved.
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