Question

Which of the following is an identity?

A. csc²x + cot²x = 1
B. (cscx + cotx)2 = 1
C. sin²x-cos²x = 1
D. sin²x sec²x + 1 = tan²x csc²x

Answer 1

Explanation:

it is D as

L.H.S.=sin²x sec²x+1

`(sin^2x)/(cos^2x) +1\\=(sin^2x+cos^2x)/(cos^2x) \\=(1)/(cos^2x) \\=sec^2x`

again

`R.H.S.=tan^2x csc^2x\\=(sin^2x)/(cos^2x) * (1)/(sin^2x) \\=(1)/(cos^2x) \\=sec^2x`

L.H.S.=R.H.S.