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Verify the following trig identities​.

Verify the following trig identities​.-example-1

1 Answer

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Answer:

see explanation

Explanation:

Using the trigonometric identities

• 1 + cot² x = csc²x and csc x =
(1)/(sinx)

• sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Consider the left side

sin²Θ( 1 + cot²Θ )

= sin²Θ × csc²Θ

= sin²Θ × 1 / sin²Θ = 1 = right side ⇔ verified

-----------------------------------------------------------------

Consider the left side

cos²Θ - sin²Θ

= cos²Θ - (1 - cos²Θ)

= cos²Θ - 1 + cos²Θ

= 2cos²Θ - 1 = right side ⇒ verified

User Nikita Petrenko
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