F=1
Add 22 to both sides, then divide both sides by 3
3.006 rounded to the nearest tenth is 3.0. This is due to the fact that
the 6 rounded up will mean that the current 0 becomes 1, but this will
not be carried to the tenth when rounding up.
I believe the answer is 2.
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
<h3>
How to solve the trigonometric identity?</h3>
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
Learn more about trigonometric identities here:
brainly.com/question/27990864
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