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We can use identities to help us solve trigonometric equations. Using a Pythagorean identity we see that the equation sin(x) + sin2(x) + cos2(x) = 1 is equivalent to the basic equation Incorrect: Your answer is incorrect. whose solutions are x = Incorrect: Your answer is incorrect. for any integer k.

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Answer:

[tex]\sin x = 0[/tex], [tex]x = \pm \pi\cdot i[/tex], [tex]\forall i \in \mathbb{N}_{O}[/tex]

Step-by-step explanation:

The following trigonometric equation is simplified by using identities:

[tex]\sin x + \sin^{2}x + \cos^{2}x = 1[/tex]

[tex]\sin x + 1 = 1[/tex]

[tex]\sin x = 0[/tex]

Whose solutions are:

[tex]x = \pm \pi\cdot i[/tex], [tex]\forall i \in \mathbb{N}_{O}[/tex]

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