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ASHA 777 [7]
2 years ago
6

Verify csc^2t-cos t sect= cot^2 t

Mathematics
2 answers:
Ymorist [56]2 years ago
7 0

Rewriting the left hand side,

csc²t - cost sec t

= (1/sin²t)-(cost)(1/cost)

= 1/sin²t - 1

= 1/sin²t - sin²t/sin²t

= (1-sin²t)/sin²t

= cos²t/sin²t

= cot²t

nata0808 [166]2 years ago
6 0

Step-by-step explanation:

assuming this is correct, you can really manipulate either side and you should arrive eventually arrive to same sides. But in this case you usually manipulate the more complex side. So I'll manipulate the left side.

Original Equation:

csc^2(t)-cos(t)*sec(t)=cot^2(t)

Rewrite csc and sec, using the reciprocal identities:

(\frac{1}{sin(t)})^2-cos(t)*\frac{1}{cos(t)}=cot^2(t)

multiply cos(t) and 1/cos(t) and also distribute the exponent:

\frac{1}{sin^2t}-1=cot(t)^2

Multiply 1 by sin^2(t)/sin^2(t)

\frac{1}{sin^2(t)}-\frac{sin^2(t)}{sin^2(t)}

subtract the numerator

\frac{1-sin^2(t)}{sin^2(t)}

Pythagorean Identity:

sin^2(t)+cos^2(t)=1

subtract sin^2(t) from both sides

cos^2(t)=1-sin^2(t)

Use this to rewrite the numerator:

\frac{cos^2(t)}{sin^2(t)}

Rewrite using the reciprocal identities:

cot^2(t) = cot^2(t)

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2 years ago
Is<br>Five times what number plus 10 equals 20<br>​
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2

Step-by-step explanation:

5*2=10

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3 0
3 years ago
Read 2 more answers
Danny made a mistake in the following problem.
mixas84 [53]
Line 3
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7 0
3 years ago
The number of employees per department are normally distributed with a population standard deviation of 198 employees and an unk
cricket20 [7]

Answer:

EBM = +-54.126

Step-by-step explanation:

In this question we have confidence interval to be 80%

The formula to solve this is in the attachment.

Bar X = 1460

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n = 22 departments

After we have inserted all values in to the formula we have:

1460 +-(1.282*198/√22)

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6 0
3 years ago
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