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What will be the value of 2cos2 θ - 1, if cos4 θ - sin4 θ = 2/3?
- a)1
- b)2
- c)3/2
- d)2/3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What will be the value of 2cos2θ - 1, if cos4θ - sin4&thet...
Given cos4 θ - sin4 θ = 2/3
Now, here we can apply the formula -
a4 - b4 = (a2 - b2) (a2 + b2)
So, (cos2 θ - sin2 θ) (cos2 θ + sin2 θ) = 2/3
So, 1 x (cos2 θ - sin2 θ) = 2/3 (because cos2 θ + sin2 θ = 1)
⇒ cos2 θ - (1 - cos2 θ) = 2/3 (because sin2 θ = 1 - cos2 θ)
So, 2cos2 θ - 1 = 2/3
Now, here we can apply the formula -
a4 - b4 = (a2 - b2) (a2 + b2)
So, (cos2 θ - sin2 θ) (cos2 θ + sin2 θ) = 2/3
So, 1 x (cos2 θ - sin2 θ) = 2/3 (because cos2 θ + sin2 θ = 1)
⇒ cos2 θ - (1 - cos2 θ) = 2/3 (because sin2 θ = 1 - cos2 θ)
So, 2cos2 θ - 1 = 2/3
Most Upvoted Answer
What will be the value of 2cos2θ - 1, if cos4θ - sin4&thet...
It appears that the expression "2cos2" is incomplete and does not make mathematical sense. In order to provide an answer, please provide the full expression or specify what you are referring to.
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Community Answer
What will be the value of 2cos2θ - 1, if cos4θ - sin4&thet...
Given cos4 θ - sin4 θ = 2/3
Now, here we can apply the formula -
a4 - b4 = (a2 - b2) (a2 + b2)
So, (cos2 θ - sin2 θ) (cos2 θ + sin2 θ) = 2/3
So, 1 x (cos2 θ - sin2 θ) = 2/3 (because cos2 θ + sin2 θ = 1)
⇒ cos2 θ - (1 - cos2 θ) = 2/3 (because sin2 θ = 1 - cos2 θ)
So, 2cos2 θ - 1 = 2/3
Now, here we can apply the formula -
a4 - b4 = (a2 - b2) (a2 + b2)
So, (cos2 θ - sin2 θ) (cos2 θ + sin2 θ) = 2/3
So, 1 x (cos2 θ - sin2 θ) = 2/3 (because cos2 θ + sin2 θ = 1)
⇒ cos2 θ - (1 - cos2 θ) = 2/3 (because sin2 θ = 1 - cos2 θ)
So, 2cos2 θ - 1 = 2/3
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What will be the value of 2cos2θ - 1, if cos4θ - sin4θ = 2/3?a)1b)2c)3/2d)2/3Correct answer is option 'D'. Can you explain this answer?
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