2 years ago

Simplify the trigonometric expression sin(4x) +2 sin(2x) using Double-Angle Identities.

Mathematics

1 answer:

emmasim [6.3K]2 years ago

6 0

Answer:

8sin(x)cos³(x)

Step-by-step explanation:

sin(4x) +2 sin(2x) = 2sin(2x)*cos(2x) + 2sin(2x) = 2sin(2x)(cos2x + 1)=

= 2sin(2x)(cos²x - sin²x + cos²x + sin²x)=²2sin(2x)*(2cos²x)=

= 4*2sin(x)*cos(x)*cos²(x)= 8sin(x)cos³(x)

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(√2)^3<br><img src="https://tex.z-dn.net/?f=%20%28%5Csqrt%7B2%29%20%7B%3F%7D%5E%7B3%20%5C%5C%7D%20" id="TexFormula1" title=" (\s

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$\sf \left(\sqrt{2}\right)^3\\\\\\\\\boxed{\sf \mathrm{Apply\:radical\:rule}:\quad \sqrt{a}=a^{\frac{1}{2}}}\\\\\\\\\sf \left(2^{\frac{1}{2}}\right)^3\\\\\\\\\boxed{\sf\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc} }\\\\\\\\\sf \sf 2^{\frac{1}{2}\cdot \:3}\\\\\\\\\sf 2^{\frac{3}{2}}\\\\\\\\\sf 2^{\frac{3}{2}}=2^{1+\frac{1}{2}}\\\\\\\\\sf 2^{1+\frac{1}{2}}\\\\\\\\\boxed{\sf \mathrm{Apply\:exponent\:rule}:\quad \:x^{a+b}=x^ax^b}\\\\\\\\\sf$