Prove that cos - sin = v2 sin , Mathematics

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?.

 

Posted Date: 4/9/2013 1:12:00 AM | Location : United States







Related Discussions:- Prove that cos - sin = v2 sin , Assignment Help, Ask Question on Prove that cos - sin = v2 sin , Get Answer, Expert's Help, Prove that cos - sin = v2 sin Discussions

Write discussion on Prove that cos - sin = v2 sin
Your posts are moderated
Related Questions
Comparison Test for Improper Integrals Here now that we've seen how to actually calculate improper integrals we should to address one more topic about them.  Frequently we ar

I need help with direct variation between x and y

Value Of The Game The game value refers to the average pay off per play of the game over an extended period of time

Example of Subtraction of Fractions: 1/3 + 1/6 + 1/8 = ____ Using trial & error we could search that 24 is the LCD or smallest number in which 3, 6, and 8 will all divide w

The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.

What is 124 out of 300 in percent ?

Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n

The area of a parallelogram is x 8 . If the base is x 4 , what is the height in terms of x? Since the area of a parallelogram is A = base times height, then the area divided by

A valid identifier in the programming language FORTAN contains a string of one to six alphanumeric characters (the 36 characters A, B,...., Z, 0, 1,...9) starting with a letter. De

Case 1: Suppose we have two terms 8ab and 4ab. On dividing the first by the second we have 8ab/4ab = 2 or 4ab/8ab = (1/2) depending on whether we consider either 8ab or 4ab as the