1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fredd [130]
3 years ago
10

(1+tanx)/(sinx+cosx)=secx

Mathematics
1 answer:
jek_recluse [69]3 years ago
5 0

\frac{1+\tan x}{\sin x+\cos x}=\sec x is proved

<h3><u>Solution:</u></h3>

Given that,

\frac{1+\tan x}{\sin x+\cos x}=\sec x  ------- (1)

First we will simplify the LHS and then compare it with RHS

\text { L. H.S }=\frac{1+\tan x}{\sin x+\cos x}  ------ (2)

\text {We know that } \tan x=\frac{\sin x}{\cos x}

Substitute this in eqn (2)

=\frac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}

On simplification we get,

=\frac{\frac{\sin x+\cos x}{\cos x}}{\sin x+\cos x}

=\frac{\sin x+\cos x}{\cos x} \times \frac{1}{\sin x+\cos x}

Cancelling the common terms (sinx + cosx)

=\frac{1}{c o s x}

We know secant is inverse of cosine

=\sec x=R . H . S

Thus L.H.S = R.H.S

\frac{1+\tan x}{\sin x+\cos x}=\sec x

Hence proved

You might be interested in
Look at the figure below: Triangle ABC is a right triangle with angle ABC equal to 90 degrees. The length of AC is 7 units, and
Studentka2010 [4]

Answer: 12.25

Step-by-step explanation:

Given the following details :

DAC = 90° and ABC = 90° = right angled

Segment AB is Parallel to segment DC

FROM THE DETAILS ;

Triangle ABC and ACD are similar triangles.

Length AC = 7 Units

Length AB = 4 Units

For similar triangles :

Segment CD /AC = Segment AC / AB

CD / 7 = 7 / 4

Cross multiply

CD × 4 = 7 × 7

CD × 4 = 49

CD = 49 / 4

CD = 12.25 Units

3 0
3 years ago
Celia filled the glasses shown below completely with water. The total amount of water that Celia poured into the glasses is 80 c
bagirrra123 [75]
The height of glass 1 is 7.6
so, you find the volume of glass 2,= 26.376
then you subtract the answer from 80 cubic cm to get the volume of glass 1
                           80 - 26.376 = 53.694
then you work backwards to get the height, which is 7.6
7 0
3 years ago
Read 2 more answers
5. Luis found a new text messaging plan which will charge him $2.00 for 80 messages. Using this
Pavel [41]
I think that Luis would have to pay $22.50
7 0
2 years ago
Determine whether the following statement is true or false. Then, use complete sentences to explain your answer. If you wish, yo
chubhunter [2.5K]

Answer:

False

Step-by-step explanation:

An acute angle can be scalene

Eg - 2 angles of 20 degrees , and 1 angle of 50 degre

HOPE THIS WILL HELP YOU

8 0
3 years ago
Can somebody help me?
nikdorinn [45]

Answer:

D

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • What’s the answer? Please help me
    10·1 answer
  • Circle A has a diameter of 9 inches, a circumference of 28.26 inches, and an area of 63.585 square inches. The diameter of circl
    5·1 answer
  • Point A (2,5) is dilated from the Irgun with the scale factor 3, resulting in point A'. Darius says the coordinates of point A a
    5·2 answers
  • Carmen paid $17.64 for a 7.94-ky bag of dog food. A few weekel later, she paid $18.88 for an 8,39 ky bag at a different store,
    15·1 answer
  • Step by step how do you solve ratios and proportions?
    11·1 answer
  • B. 13(y−10)=−4<br> 1<br> 3<br> (<br> y<br> -<br> 10<br> )<br> =<br> -<br> 4<br> y =
    5·1 answer
  • Can someone help me with this
    7·2 answers
  • 12) Kyle bought onions at $0.96 per pound. He paid $4.32<br> total. How many pounds did he buy?
    10·1 answer
  • A sum of money was shared between Joan and Ngozi in the ratio 5:3. If Joan share was 40.00naira how much was the original sum of
    5·1 answer
  • A field is a rectangle with a perimeter of 1110 feet. The length is 100 feet mora than the width. Find the width and length of t
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!