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If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?.
Ans: Cos? + Sin? = √2 Cos?
⇒ ( Cos? + Sin?)2 = 2Cos2?
⇒ Cos2? + Sin2?+2Cos? Sin? = 2Cos2?
⇒ Cos2? - 2Cos? Sin?+ Sin2? = 2Sin2? ( ∴2Sin2? = 2 - 2Cos2?)
⇒ (Cos? - Sin?)2 = 2Sin2? (1- Cos2? = Sin2? & 1 - Sin2? = Cos2?)
or Cos? - Sin? = √2 Sin?.
Suppose that the number of hours Katie spent practicing soccer is represented through x. Michael practiced 4 hours more than 2 times the number of hours that Katie practiced. How l
x=±4, if -2 = y =0 x=±2, if -2 = y = 0
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1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent
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Determine whether the following numbers are odd or even: Examples: Determine whether the following numbers are odd or even: 364, 1068, & 257. Solution: 1.
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