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Romashka [77]
3 years ago
5

PLEASE HELP ASAP IM PANICKING :(((

Mathematics
1 answer:
Inessa [10]3 years ago
7 0

Answer:

A

Step-by-step explanation:

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3 sin ^2 x - 3 sin ^4 x =0
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I assume you're just solving for x. Factorize the left side as

3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0

Recall that

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so that the equation further reduces to

3 sin²(x) cos²(x) = 0

Also recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

which lets us rewrite the equation as

3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0

Solve for x :

3/4 sin²(2x) = 0

sin²(2x) = 0

sin(2x) = 0

2x = arcsin(0) + 2nπ   or   2x = π - arcsin(0) + 2nπ

(where n is any integer)

2x = 2nπ   or   2x = (2n + 1) π

x = nπ   or   x = (2n + 1)/2 π

Notice that this means the solution set is

{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}

so we can condense the solution further to

x = nπ/2

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