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Mathematics

2 answers:

katen-ka-za [31]3 years ago

8 0

Answer:

Step-by-step explanation:

Mazyrski [523]3 years ago

7 0

Answer:

2x + 19.

Step-by-step explanation:

The reasoning behind this is that one must find the disparity between the first and second expressions - 9x+14 and 7x-5. To do this, one subtracts 7x-5 from 9x+14. Set this up as though it were a normal subtraction problem - 9x+14 over 7x-5 with the little subtraction symbol to the left. When subtracting the negative five from fourteen, one adds the five to the fourteen due to the fact that the five was already negative and as such the negatives cancel out. The 7x is simply subtracted from the 9x, resulting in 2x. This leads to 2x + 19.

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3 years ago

Show that cos(3theta) = 4cos3(theta) − 3cos (theta).

Delvig [45]

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

To prove:

$\cos 3\theta=3\cos^3 \theta-3\sin^2 \theta\cos \theta$

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)

$\sin^2A+\cos^2A=1$ .......(4)

Taking the LHS:

$\Rightarrow \cos 3\theta=\cos (\theta +2\theta )$

Using identity 1:

$\Rightarrow \cos (\theta +2\theta )=\cos \theta \cos 2\theta-\sin \theta \sin 2\theta$

Using identities 2 and 3:

$\Rightarrow \cos \theta (\cos ^2\theta-\sin^2 \theta )-\sin \theta (2\sin \theta \cos \theta )\\\\\Rightarrow \cos^3\theta -\sin^2\theta \cos \theta -2\sin^2 \theta \cos \theta \\\\\Rightarrow \cos^3\theta -3\sin^2\theta \cos \theta$

Using identity 4:

$\Rightarrow \cos^3\theta -3(1-\cos^2\theta) \cos \theta\\\\\Rightarrow \cos^3\theta-3\cos \theta+3\cos^3\theta\\\\\Rightarrow 4\cos^3\theta -3\cos \theta$