Question

5. Prove : tan²0 + cot+0 + 2 = sec20-cosec-0.​

Answer 1

[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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