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ryzh [129]
3 years ago
11

Precalculus Homework help please.

Mathematics
1 answer:
aniked [119]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

(5)

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cos²x = 1 - sin²x

Given

3sin²Θ + 2cos²Θ - 2

= 3sin²Θ + 2(1 - sin²Θ) - 2

= 3sin²Θ + 2 - 2sin²Θ - 2

= sin²Θ

(6)

Using the trigonometric identity

secx = \frac{1}{cosx}

Consider the left side

\frac{cosx}{1-sin^2x}

= \frac{cosx}{cos^2x}

= \frac{1}{cosx} = secx = right side ⇒ verified

(7)

Using the trigonometric identity

1 + cot²x = csc²x

Given

sin²x. cot²x + sin²x ← factor out sin²x from each term

= sin²x(cot²x + 1)

= sin²x. csc²x

= sin²x × \frac{1}{sin^2x} = 1

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