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3 years ago

Prove that sec^2θcosec*2θ-2-cot^2θ=tan2θ

Mathematics

1 answer:

Tema [17]3 years ago

5 0

Answer:

Step-by-step explanation:

I think you mean tan^2θ, not tan2θ.

Use the trigonometric identities

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

sin²θ = 1-cos²θ

cos²θ = 1-sin²θ

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The definitions of sine, cosine, and tangent

Aloiza [94]

sine: the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.
cosine: the trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.
tangent: a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.

8 0

3 years ago

Read 2 more answers

HELP!!! A cell phone is 132 mm long and 57 mm wide. What is ratio of the width and length in simplest form.

GalinKa [24]

The ratio of width to length in simplest form is 19 : 44

Solution:

Given that, A cell phone is 132 mm long and 57 mm wide

Length of cell phone = 132 mm

Width of cell phone = 57 mm

We have to find the ratio of width and length in simplest form

$\frac{Width}{Length} = \frac{57}{132}\\\\\text{Reduce to lowest terms }\\\\\frac{width}{length} = \frac{57 \div 3}{132 \div 3}\\\\\frac{Width}{Length} = \frac{19}{44}$

In ratio form, we know that,

$\frac{a}{b} = a : b$

Writing in ratio form, we get

Width : length = 19 : 44

Thus the ratio of width to length in simplest form is 19 : 44

6 0

3 years ago

Daniel's basic cell phone rate each month is $29.95. Add to that $5.95 for voice mail and $2.95 for text messaging. This past mo

Vlad [161]

5.95 + 2.95 = 8.9
8.9 + 29.95 = 38.85
62.35 - 38.85 = 23.5
So Daniel spent $23.50 on long distance calling

8 0

4 years ago

Read 2 more answers

On a cold day, hailstones fall with a velocity of 2i − 6k m s−1 . If a cyclist travels through the hail at 10i m s−1 , what is t

Paraphin [41]

Answer:

The velocity of the hail relative to the cyclist is $V_{hc}=-8\hat{i}-6\hat{k}$

The angle at which hailstones falling relative to the cyclist is $\theta = 36.86^\circ$

Step-by-step explanation:

Given : On a cold day, hailstones fall with a velocity of $2\hat{i}-6\hat{k}\text{ m/s}$ . If a cyclist travels through the hail at $10\hat{i} \text{ m/s}$ .