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2 years ago

Verify that [tan(theta) + cot(theta)]^2 = sec^2(theta) + csc^2(theta)

Mathematics

1 answer:

Wittaler [7]2 years ago

7 0

(tanθ + cotθ)² = sec²θ + csc²θ

Expand left side: tan²θ + 2tanθcotθ + cot²θ

Evaluate middle term: 2tanθcotθ = $2*\frac{sin\theta}{cos\theta}*\frac{cos\theta}{sin\theta}$ = 2

⇒ tan²θ + 2+ cot²θ

= tan²θ + 1 + 1 + cot²θ

Apply trig identity: tan²θ + 1 = sec²θ

⇒ sec²θ + 1 + cot²θ

Apply trig identity: 1 + cot²θ = csc²θ

⇒ sec²θ + csc²θ

Left side equals Right side so equation is verified

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kiruha [24]

Answer: Choice D

In two games, the team lost to the opponent by 1 goal.

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Explanation:

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So a difference of -1 means the team lost by 1 point.

We have 2 dots over this value, so there are 2 occasions where the team lost to the opponent by 1 goal.

An example would be that say the team scored 3 goals and the opponent scored 4 goals. So we have a differential of 3-4 = -1. The order is important because we would not say 4-3 = 1.

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2 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1) , and C(2, 5) ?

KatRina [158]

The circumcenter is where the perpendicular bisectors meet.
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one perpendicular bisector is x=1, another perpendicular bisector is y=3
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3 years ago

Find the measure of each angle.

Galina-37 [17]

Given:

Given that the isosceles trapezoid JKLM.

The measure of ∠K is 118°

We need to determine the measure of each angle.

Measure of ∠L:

By the property of isosceles trapezoid, we have;

$\angle K+\angle L=180^{\circ}$

$118^{\circ}+\angle L=180^{\circ}$

$\angle L=62^{\circ}$

Thus, the measure of ∠L is 62°

Measure of ∠M:

By the property of isosceles trapezoid, we have;

$\angle L \cong \angle M$

Substituting the value, we get;

$62^{\circ}=\angle M$

Thus, the measure of ∠M is 62°

Measure of ∠J:

By the property of isosceles trapezoid, we have;

$\angle J \cong \angle K$

Substituting the value, we get;

$\angle J =118^{\circ}$

Thus, the measure of ∠J is 118°

Hence, the measures of each angles of the isosceles trapezoid are ∠K = 118°, ∠L = 62°, ∠M = 62° and ∠J = 118°

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2 years ago

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A rectangle has a width of 10 feet and a length of 40 feet. What is the length of the side of a square with the same area?

never [62]

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