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3 years ago

Show that sinx/1+cosx=tanx/2

Mathematics

1 answer:

hammer [34]3 years ago

7 0

Answer:

See proof below

Step-by-step explanation:

show that

sinx/1+cosx=tanx/2

From LHS

sinx/1+cosx

According to half angle

sinx = 2sinx/2 cosx/2

cosx = cos²x/2 - sin²x/2

cosx = cos²x/2 - (1- cos²x/2)

cosx = 2cos²x/2 - 1

cos x + 1 = 2cos²x/2

Substitute into the expression;

sinx/1+cosx

= (2sinx/2 cosx/2)/2cos²x/2

= sinx.2/cos x/2

Since tan x = sinx/cosx

Hence sinx/2/cos x/2 = tan x/2 (RHS)

This shows that sinx/1+cosx=tanx/2

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3 years ago

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3 years ago

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4 years ago

12. Ms. Smith keeps eight different cookbooks on a shelf in one of her kitchen cabinets. How many ways can the eight cookbooks b

Ghella [55]

Answer:

The number of ways are 40320.

Step-by-step explanation:

Consider the provided information.

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6 0

4 years ago

Myra is a scientist and needs 45 gallons of a 16% acid solution. The lab is currently stocked only with a 20% acid solution and

asambeis [7]

Answer:

The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons

Step-by-step explanation:

Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:

x + y = 45

The concentration of acid of the final solution is:

0.2*x + 0.1*y = 45*0.16

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Therefore we have a system of equation:

x + y = 45

0.2*x + 0.1*y = 7.2

We need to multiply the first equation by -0.1:

-0.1*x -0.1*y = -4.5

0.2*x + 0.1*y = 7.2

We now sum both equation:

0.1*x = 2.7

x = 2.7/0.1 = 27 gallons

y = 45 - 27 = 18 gallons

6 0

4 years ago

Show that sinx/1+cosx=tanx/2​

Show that sinx/1+cosx=tanx/2