Prove that cos - sin = v2 sin , Mathematics

Assignment Help:

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?.

Related Discussions:- Prove that cos - sin = v2 sin

Eometyr, Lines EF and GH are graphed on this coordinate plane. Which point ...

Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?

SAT question, In a certain class, one half of the male students and two thi...

In a certain class, one half of the male students and two thirds of the female students speak French. If there are three fourths as many girls as boys in the class. What fraction o

Buyer behaviour, buyer behaviour

buyer behaviour

Find the curve on the surface - shortest arc lenght, (a) Find the curve on ...

(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an

What is her weekly paycheck assuming there are deductions, Kyra's weekly wa...

Kyra's weekly wages are $895. A Social Security tax of 7.51% and a State Disability Insurance of 1.2% are taken out of her wages. What is her weekly paycheck, assuming there are no

Angles, how to measure missing angle of an adjacent angle

how to measure missing angle of an adjacent angle

determine that the relation is symmetric and transitive, 1. Let R and S be...

1. Let R and S be relations on a set A. For each statement, conclude whether it is true or false. In each case, provide a proof or a counterexample, whichever applies. (a) If R

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Initial condition for differential equations, Initial Condition(s) are a se...

Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after. Initial conditions are frequently a

Light take 5.3 × 10-6 seconds calculate standard notation, It takes light 5...

It takes light 5.3 × 10 -6 seconds to travel one mile. What is this time in standard notation? In order to convert this number to standard notation, multiply 5.3 through the f

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages