The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
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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:
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Answer:
false statement
Step-by-step explanation:
5+x^2=2x^2+13
5+x^2-2x-13=0
-8+x^2-2x^2=0
-8-x^2=0
-x^2=8
x^2=-8
this statement is false for any value of x because the power function with an even exponent is always postive or 0
Answer:
500 points
Step-by-step explanation:
In the first game the participant got 300 points and in the second game the participant got 200 points. The total score is both games added together. 300 + 200 is 500. 500 points is his total score.
Answer:
22 hours
Step-by-step explanation:
Ken saves 90% of his earnings.
So, he must earn
270/x =90/100
90x=270*100
90x=27,000
x=27000/90
=300
x=$300 to save $270
For starting 10hours, Ken earns $8 per hour so he earns total
$8*10 hours=$80
Now, Ken has to earn remaining
$220 at a rate of $10/hour, he must work for at least
$220/$10
=22hours
It’s a meteor When meteoroids enter Earth's atmosphere (or that of another planet, like Mars) at high speed and burn up, the fireballs or “shooting stars” are called meteors. When a meteoroid survives a trip through the atmosphere and hits the ground, it's called a meteorite.