Solve $cos 3 x {cos}^{3} x + sin 3 x {sin}^{3} x = 0$ .

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Solution

we get $4 {cos}^{3} 2 x = 0$
$∴ cos 2 x = 0$
or $2 x = (n + \frac{1}{2}) π$ or $x = (n + \frac{1}{2}) \frac{π}{2}$ .

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cos 3 x {cos}^{3} x + sin 3 x {sin}^{3} x = 0

Q. Prove

sin 3 x {sin}^{3} x + cos 3 x {cos}^{3} x = {cos}^{3} 2 x .

Q.
lf

{sin}^{3} x sin 3 x = n \sum m = 0 C_{m} {cos}^{m} x

; where

C_{0}, C_{1}, C_{2} \dots \dots . . C_{n}

are constants and

C_{n} \neq 0,

then

n =

Q. If

s i n^{3} x s i n 3 x = \sum_{m = 0}^{n} C_{m} c o s m x

where

c_{0}, c_{1}, c_{2}, . . . . . . . . . . . c_{n}

are constants and

C_{n} \neq 0

,then the value of n is

$I f s i n^{3} x s i n 3 x = \sum_{m = 0}^{n} c_{m} c o s m x w h e r e c_{0}, c_{1}, c_{2} . \dots \dots, c_{n} a r e c o n s t a n t s a n d c_{n} \neq 0, t h e n t h e v a l u e o f n i s$

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Solve cos3xcos3x+sin3xsin3x=0.

we get 4cos32x=0∴cos2x=0or 2x=(n+12)π or x=(n+12)π2.

Solve $cos 3 x {cos}^{3} x + sin 3 x {sin}^{3} x = 0$ .

we get $4 {cos}^{3} 2 x = 0$
$∴ cos 2 x = 0$
or $2 x = (n + \frac{1}{2}) π$ or $x = (n + \frac{1}{2}) \frac{π}{2}$ .