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Precalculus Homework help please.

Precalculus Homework help please.-example-1
User RemarkLima
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3 votes

Answer:

see explanation

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 =
(1)/(cosx)

Consider the left side


(cosx)/(1-sin^2x)

=
(cosx)/(cos^2x)

=
(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 ×
(1)/(sin^2x) = 1

User Rapfaria
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