Question

If f(x) = sinx. Show that f(3x) = 3f(x) - 4x^3 (x)

Answer 1

Please see the attachment

Answer 2

The given relation is proved.

$f(3x) = 3f(x) - 4f^3 (x)$

Step-by-step explanation:

We are given the following in the question:

$f(x) = \sin x$

We have to prove the following:

$f(3x) = 3f(x) - 4f^3 (x)$

LHS:

$f(3x) = \sin (3x)$

RHS:

$3f(x) - 4f^3 (x)\\=3\sin x - 4\sin^3 x$

By the trigonometric identity:

$\sin (3x) = 3\sin x - 3\sin^3 x$

Thus, we can write:

$f(3x) = 3f(x) - 4f^3 (x)$

Hence, proved.

#LearnMore

If f(x)= (x-1/x+1), then f(2x) is

A) (f(x)+1/f(x)+3)

B)(3f(x)+1/f(x)+3)

C)(f(x)+3/ f(x)+1)

D)(f(x)+3/3f(x)+1)

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