How do I show that both sides of these trigonometric identities are equal to each other?

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How do I show that both sides of these trigonometric identities are equal to each other?

1.) $sin θ = cos θ tan θ$ $sintheta = costhetatantheta$
2.) ${sin}^{2} θ - {cos}^{2} θ = 1 - 2 {cos}^{2} θ$ $sin^2theta-cos^2theta=1-2cos^2theta$

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Answer 1 · 2018-05-15T17:56:15

See explanation

Explanation:

...pretty straightforward, I think:
First one: $sin θ = cos θ tan θ$ $sin theta = cos theta tan theta$
...remember that $tan θ = \frac{sin θ}{cos θ}$ $tan theta = (sin theta) /(cos theta)$
so:
$sin θ = cos θ \cdot (\frac{sin θ}{cos θ})$ $sin theta = cos theta * ((sin theta)/(cos theta))$

...and the $cos θ$ $cos theta$ terms on the right cancel out:

$sin θ = sin θ$ $sin theta = sin theta$

What you have to do for the second one is add $2 {cos}^{2} θ$ $2cos^2 theta$
to both sides:

${sin}^{2} θ - {cos}^{2} θ + 2 {cos}^{2} θ = 1$ $sin^2 theta - cos^2 theta + 2 cos^2 theta = 1$
${sin}^{2} θ + {cos}^{2} θ = 1$ $sin^2 theta + cos^2 theta = 1$

...the above is a trig identity you should know by heart, so this shows that the original formula is a valid identity.

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How do I show that both sides of these trigonometric identities are equal to each other?

1.) $sin θ = cos θ tan θ$ $sintheta = costhetatantheta$
2.) ${sin}^{2} θ - {cos}^{2} θ = 1 - 2 {cos}^{2} θ$ $sin^2theta-cos^2theta=1-2cos^2theta$

1 Answer

Explanation:

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Humanities

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How do I show that both sides of these trigonometric identities are equal to each other?

1.) sinθ=cosθtanθsintheta = costhetatantheta 2.) sin2θ−cos2θ=1−2cos2θsin^2theta-cos^2theta=1-2cos^2theta

1 Answer

Explanation:

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1.) $sin θ = cos θ tan θ$ $sintheta = costhetatantheta$
2.) ${sin}^{2} θ - {cos}^{2} θ = 1 - 2 {cos}^{2} θ$ $sin^2theta-cos^2theta=1-2cos^2theta$