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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?.
Sketch the graphs of the following functions: (A) y = 1/(x 2 +1) (b) x= sin x,
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We desire to construct a box whose base length is three times the base width. The material utilized to build the top & bottom cost $10/ft 2 and the material utilized to build the
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