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34kurt
3 years ago
10

If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA​

Mathematics
1 answer:
Deffense [45]3 years ago
3 0

Answer:

√5.

Step-by-step explanation:

Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse  = √(1^2 + 2^2) = √5  (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).

so cos A =  adjacent / hypotenuse =   2/√5.

and sin A = opposite / hypotenuse = 1 / √5

cos A / sin A = 2/√5 /  1/ √5 =  2.

sin A / (1 + cos A) =  1/√5 (1 + 2/ √5)

=  1 / √5 ( (√5 + 2) /√5)

= 1 / (√5 + 2)

So the answer is:

2  +   1 /(√5 + 2).

We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.

2 + 1 / (√5 + 2)

= 2(√5 + 2) + 1 / (√5 + 2 )

= { 2(√5 + 2) + 1 } /  (√5 + 2)

Multiplying this by  √5 - 2 / √5 - 2 we get:

(2(5 - 4) + √5 - 2) /  (5 -4)

=  2 + √5 - 2 / 1

= √5.

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4 0
3 years ago
(9x²+24x-8)-(5x²+3x+10)
Thepotemich [5.8K]

Answer:

4x^2 + 21x - 18

Step-by-step explanation:

(9x^2+24x-8)-(5x^2+3x+10)

9x^2+24x-8-5x^2-3x-10

9x^2 - 5x^2 = 4x^2

24x - 3x = 21x

-8 - 10 = -18

Answer: 4x^2 + 21x - 18

4 0
3 years ago
a new bank customer with $3,000 wants to open a money market account the bank is offering a simple interest rate of 1.8%....How
MArishka [77]

Answer:

$91,620

Step-by-step explanation:

1.8% = $54

$3000 + $54 = $3054

$3054 × 30 = $91,620

Hope this helped!

5 0
3 years ago
PLS HELP ME FIND WHAT A AND B EQUAL
Anarel [89]

Answer:

A = 68

B = 44

Step-by-step explanation:

The sum of the angles of a triangle add to 180

A+B+C =180

x + x-24 +68 = 180

Combine like terms

2x+44 =180

Subtract 44 from each side

2x+44-44= 180-44

2x = 136

Divide by 2

2x/2 = 136/2

x = 68

A = x = 68

B = x-24 =44

3 0
3 years ago
Read 2 more answers
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