For each expression in Column I, choose the expression from Column II that completes an identity.
6. sec² x = ____

II
A. sin ^2 x/cos ^2 x
B.1/(sec ^2 x)
C. sin (-x)
D. csc ^2 x-cot ^2 x + sin ^2 x
E. tan x

검증된 단계별 안내

Recall the Pythagorean identity involving secant and tangent: \(\sec^2 x = 1 + \tan^2 x\).

Understand that this identity comes from dividing the fundamental identity \(\sin^2 x + \cos^2 x = 1\) by \(\cos^2 x\).

Rewrite the expression \(\sec^2 x\) in terms of tangent using the identity: \(\sec^2 x = 1 + \tan^2 x\).

Compare the given expression \(\sec^2 x\) with the options in Column II to find the one that matches \(1 + \tan^2 x\).

Select the expression from Column II that completes the identity as \(1 + \tan^2 x\).

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Pythagorean Identity

The Pythagorean identities relate the squares of sine, cosine, and secant functions. One key identity is 1 + tan²x = sec²x, which expresses sec²x in terms of tan²x. This identity is fundamental for transforming and simplifying trigonometric expressions.

Definition of Secant Function

Secant (sec x) is the reciprocal of cosine, defined as sec x = 1/cos x. Understanding this reciprocal relationship helps in manipulating expressions involving sec²x and connecting them to other trigonometric functions like cosine and tangent.

Trigonometric Function Squares

Squaring trigonometric functions, such as sec²x or tan²x, is common in identities and equations. Recognizing how these squares relate through identities allows for simplification and solving of trigonometric problems effectively.

For each expression in Column I, choose the expression from Column II that completes an identity.6. sec² x = ____IIA. sin ^2 x/cos ^2 xB.1/(sec ^2 x)C. sin (-x)D. csc ^2 x-cot ^2 x + sin ^2 xE. tan x