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Fed [463]
2 years ago
7

Question 17 of 30

Health
1 answer:
cestrela7 [59]2 years ago
8 0
A. Learn proper safety skills
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90 pounds...................

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5. Explain the structure of the heart. nations of the heart​
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3 years ago
9.<br>(1 + tan²theta) cot theta<br>cosec theta<br>tan theta​
wolverine [178]

Answer:

Proved

Explanation:

Given

\frac{(1+tan^2\theta). cot\theta}{cosec^2 \theta}= tan \theta

Required

Prove

In trigonometry:

1 + tan^2\theta = sec^2\theta

So, we have:

\frac{sec^2\theta *  cot\theta}{cosec^2 \theta}= tan \theta

Express each identity as an inverse:

\frac{\frac{1}{cos^2\theta} *  \frac{1}{tan\theta}}{\frac{1}{sin^2 \theta}}= tan \theta

Rewrite as:

(\frac{1}{cos^2\theta} *  \frac{1}{tan\theta})/ \frac{1}{sin^2 \theta}= tan \theta

Express tan as sin/cos:

(\frac{1}{cos^2\theta} *  \frac{1}{sin\theta/cos\theta})/ \frac{1}{sin^2 \theta}= tan \theta

(\frac{1}{cos^2\theta} *  \frac{1}{sin\theta/cos\theta}) * sin^2 \theta= tan \theta

(\frac{1}{cos^2\theta} *  \frac{cos\theta}{sin\theta}) * sin^2 \theta= tan \theta

(\frac{1}{cos\theta} *  \frac{1}{sin\theta}) * sin^2 \theta= tan \theta

\frac{sin^2 \theta}{cos\theta*sin\theta}= tan \theta

\frac{sin \theta}{cos\theta}= tan \theta

tan \theta= tan \theta

Proved

3 0
3 years ago
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