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Kitty [74]
3 years ago
11

Verify the identity. cosine theta minus secant thetaequalsnegative sine theta tangent theta to verify the​ identity, start with

the more complicated side and transform it to look like the other side. choose the correct transformations and transform the expression at each step.
Mathematics
1 answer:
krok68 [10]3 years ago
4 0
I will use x for theta.

-sinx tanx = -sinx (sinx/ cosx) =
-sin²x / cosx = (cos²x - 1) / cosx = cosx - secx

and done. if there is some part you don't understand just ask!!
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given that sin theta= 1/4, 0 is less than theta but less than pi/2, what is the exact value of cos theta
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Answer:

\cos{\theta} = \frac{\sqrt{15}}{4}

Step-by-step explanation:

For any angle \theta, we have that:

(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1

Quadrant:

0 \leq \theta \leq \frac{\pi}{2} means that \theta is in the first quadrant. This means that both the sine and the cosine have positive values.

Find the cosine:

(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1

(\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1

\frac{1}{16} + (\cos{\theta})^{2} = 1

(\cos{\theta})^{2} = 1 - \frac{1}{16}

(\cos{\theta})^{2} = \frac{16-1}{16}

(\cos{\theta})^{2} = \frac{15}{16}

\cos{\theta} = \pm \sqrt{\frac{15}{16}}

Since the angle is in the first quadrant, the cosine is positive.

\cos{\theta} = \frac{\sqrt{15}}{4}

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