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hichkok12 [17]
3 years ago
10

Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum

Mathematics
1 answer:
otez555 [7]3 years ago
4 0

<u>Step-by-step explanation:</u>

To prove:

\cos 3x=\cos^3x-3\sin^2 x\cos x

Identities used:

\cos(A+B)=\cos A\cos B+\sin A\sin B      ......(1)

\sin 2A=2\sin A\cos A        ........(2)

\cos 2A=\cos^2A-\sin^2 A     .......(3)

Taking the LHS:

\Rightarrow \cos 3x=\cos (x+2x)

Using identity 1:

\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x

Using identities 2 and 3:

\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x

As, LHS = RHS

Hence proved

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