Unit 5- proving identities

Hi everyone. This is manveer Today I will be blogging about the things that we went over in class but very briefly. I don't like to talk to much so I will go straight into it.

Proving Identities :

Know these strategies :  
1) Use known identities i.e. ( sinx/cosx = tanx)
2) Use the Pythagorean Identity or one of its alternate forms
3) Rewrite the equation/expression using sin and cos
4)Multiply the numerator and denominator by the conjugate
5) FACTOR

So let's begin with the first question .

To determine the non-permissible values we need to know when sinx ≠ 0 .

x ≠ 0 ,180 , 360

The general solution for this equation would be x≠180n , where nEI

To verify the equation we need to substitute our x values. In this case x=30

1-sin²x  = sinxcosxcotx

L.H.S    = 1-sin²(30)

             = 1-(1/2)²

             = 1- 1/4

             = 3/4

R.H.S   = sin(30)cos(30)cot(30) 

            = (1/2) ( √3/2) (√3)

            = 3/4

So now according to the results we can tell that L.H.S = R.H.S

Lastly , to prove that the identity is true for all the permissible values of x we need to simply the equation.
1-sin²x  = sinxcosxcotx
cos²x = sinx * cosx * cosx/sinx
cos²x = cosx*cosx
cos²x = cos²x

That's it !

Since this was a tricky question and it was a TRAP for all of us, I thought of reminding you all again.

tan(π/2 - θ ) = cotθ

All we need to do is REPLACE θ with π/2 - θ

tan(π/2 - θ) = sin(π/2 - θ) / cos (π/2 - θ)

                   = cosθ / sinθ

                   = cotθ

There are a lot of steps for this question but I have 6 easy steps that could help you get the answer.

1) Break sin3x into sin2x + sinx

2) α=2x & β=x

3) Replace sin2x => 2sinxcosx

4) Replace cos2x => 1-2sin²x

5) Multiply inside the brackets

6) Combine like terms

MAKE SURE YOU ADD THE BRAKCETS !



here are the double angle identities don't forget them :) 

ok bye