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

asked Feb 16, 2023 164k views

5 votes

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

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1 vote

Answer:

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.

Dan Johnson answered Feb 21, 2023

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