5. Prove : tan²0 + cot+0 + 2 = sec20-cosec-0.
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[Let theta be angle A, so that it can be written easily.]
To prove-
tan²A+cot²A+2=sec²A+cosec²A
Identities need to know-
Sec²A = 1+tan²A ---------id(1)
and,
Cosec²A = 1+cot²A----id(2)
Proof-
By taking left hand side (LHS),
Tan²A+cot²A+2
= (sec²A-1)+(cosec²A-1)+2
{From id(1)and id(2)}
= sec²A-1+cosec²A-1+2
= sec²A+cosec²A-2+2
= sec²A+cosec²A
= Right Hand Side(RHS)
HENCE PROVED.
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