Question

is it correct cos5x=cos(2x+3x)

Answer 1

Heya,

cos5x = cos(2x + 3x)

This statement that you have given is totally wrong.

Bcz,

Formula of cos(A + B) = cosAcosB - sinAsinB

So, According to the formula,
cos(2x + 3x) = cos2xcos3x - sin2xsin3x

So, Now, from this we can say that cos5x ≠ cos(2x + 3x)

Let us take an example,

Let the value of x be 20°

Then,
LHS:
cos5x = cos5×20°
= cos100°

RHS:
cos(2x + 3x) = cos(2×20° + 3×20°)
= cos(40° + 60°)
Now, we will further solve this by identity,

Therefore,
cos(40° + 60°) = cos40°cos60° - sin40°sin60°

From this example we can see that,
LHS ≠ RHS

So, by taking an example this is proved that cos5x ≠ cos(2x+3x)


Hope this helps....:)

Answer 2

HELLO DEAR,

in my view it is correct

let me explain with example

e.g., cos(2x)

we also write like that cos(x+x)

we know that:-

cos(A+B) = cos A cosB-sinBsinA----(2)

and
cos 2A=cos² A-sin²B------(2)

proof:-

cos(x+x) = [cosXcosX-sinXsinX]---------using (1)

=> cos ²X - sin²X.----(3)

FROM---(2) AND --(3)


cos(2X)= COS (X+X)

hence,

R.H.S= L.H.S

now,

your questions was

cos (5X)

from above explanation

we can also write like that

cos5x=cos(2x+3x)


from the above conclusion

we get,

cos 5X = cos(2X+3X)

let x= 30°

put this value of X in both side

we get,

cos ( 5×30) = cos(2×30+3×30)

=> cos 150°=cos(60°+90°)

=> cos150°=cos150°

we can take another value of X
we get ,

both sides are equal

let X= 60°

we get,

cos(5×60°) = cos(2×60°+3×60°)

=> cos 300°=cos(120°+180°)

=> cos300°=cos 300°

from this conclusion


I HOPE ITS HELP YOU DEAR,
THANKS