# Verify the Trigonometric Identity 1/(1 - sin^2(x)) = 1 + tan^2(x) | Summary and Q&A

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March 29, 2021
by
The Math Sorcerer
Verify the Trigonometric Identity 1/(1 - sin^2(x)) = 1 + tan^2(x)

## TL;DR

The video demonstrates how to verify a trigonometric identity by starting with the right-hand side and using addition and memorized formulas.

## Key Insights

• 🫱 When verifying a trigonometric identity, it is important to choose a side to start with, either the left-hand side or the right-hand side.
• 😑 Converting trigonometric functions into their equivalent forms, such as expressing tangent as sine over cosine, can simplify the expression.
• 👻 Adding terms with the same denominator allows for further simplification.

## Transcript

in this problem we're being asked to verify this trig identity let's go ahead and go through it so solution so when verifying trig identities we have to pick a side to start with so we have a choice we can start with the left hand side we can start with the right hand side so i'm looking at this and i haven't done it yet but i think in this case it... Read More

### Q: Why does the speaker choose to start with the right-hand side in verifying the trigonometric identity?

The speaker chooses to start with the right-hand side because by performing the addition, the plus sign allows for easier manipulation of the equation. Starting with the left-hand side may make it harder to simplify the expression.

### Q: How is tangent expressed in terms of sine and cosine?

Tangent can be expressed as sine over cosine. Therefore, to simplify the right-hand side, the speaker writes 1 plus tangent squared as 1 plus (sine squared x over cosine squared x).

### Q: How does the speaker convert 1 into a fraction with cosine squared as the denominator?

To convert 1 into a fraction with cosine squared as the denominator, the speaker writes it as cosine squared x over cosine squared x. This allows for the addition of terms by having the same denominator.

### Q: What is the significance of the trigonometric identities mentioned in the video?

The trigonometric identities mentioned, such as cosine squared equals 1 minus sine squared, and sine squared equals 1 minus cosine squared, are useful formulas that can be memorized to simplify trigonometric problems. They save time and allow for quicker calculations.

## Summary & Key Takeaways

• The video explains the process of verifying a trigonometric identity by selecting one side, in this case, the right-hand side, to start with.

• The right-hand side is simplified using the fact that tangent can be expressed as sine over cosine.

• By converting 1 into a fraction with cosine squared as the denominator, the addition of terms can be performed.

• The resulting expression is simplified further using the well-known trigonometric identity: cosine squared plus sine squared equals one.