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Delvig [45]
2 years ago
11

Prove the identity and include the rule

Mathematics
1 answer:
oksian1 [2.3K]2 years ago
6 0

Hi there!

To begin, we can distribute sec²x with (1 - sin²x):

= sec²x - sec²xsin²x

Which simplifies to:

= sec²x - tan²x

Recall the Pythagorean identity:

1 + tan²x = sec²x

Rearrange alike to the solved for expression above:

<u>1 = sec²x  - tan²x</u>

<u>Thus, using the Pythagorean Identity, sec²x(1 - sin²x) = 1.</u>

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Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the converse of a statement

The converse of a statement is formed by switching the hypothesis and the conclusion.

STEP 2: break down the given statements

Hypothesis: If M is the midpoint of line segment PQ,

Conclusion: line segment PM is congruent to line segment QM

STEP 3: Switch the two statements

Hence, the answer is given as:

If line segment PM is congruent to line segment QM, then M is the midpoint of line segment PQ,

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Step-by-step explanation:

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