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
Lesechka [4]
3 years ago
7

Can someone pls do 25 and 26 with working

Mathematics
1 answer:
NemiM [27]3 years ago
5 0

25.

Show

\dfrac{\tan x + \sin x}{\tan x - \sin x} = \dfrac{\sec x + 1}{\sec x - 1}

\dfrac{\tan x + \sin x}{\tan x - \sin x}

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

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

= \dfrac{\sec x + 1}{\sec x - 1} \quad\checkmark

26.

Show

\dfrac{\cot \theta + \csc \theta - 1}{\cot \theta - \csc \theta +1} = \dfrac{1+\cos \theta}{\sin \theta}

That's the cotangent half angle formula on the right, so I guess on the left too.

I fooled around with this one for a while before I took the hint which was to let \theta=2x.

\dfrac{\cot 2x + \csc 2x - 1}{\cot 2x- \csc 2x +1}

=\dfrac{ (\cos 2x / \sin 2x) + (1/\sin 2x ) - 1}{\cos 2x/\sin 2x - 1/\sin 2x + 1}

=\dfrac{\cos 2x + 1 - \sin 2x}{\cos2x - 1 + \sin 2x}

=\dfrac{2\cos^2 x - 1 + 1 -2 \cos x \sin x }{1 - 2\sin^2x-1 + 2\sin x \cos x}

=\dfrac{2 \cos^2 x -2 \cos x \sin x }{-2\sin^2x+2 \sin x \cos x}

=\dfrac{2\cos x}{2 \sin x} \cdot \dfrac{\cos x- \sin x}{-\sin x +\cos x}

=\dfrac{2\cos x}{2\sin x}

=\dfrac{2\cos^2 x}{2\sin x\cos x}

=\dfrac{1 + 2\cos^2 x - 1}{2\sin x\cos x}

= \dfrac{1 + \cos 2x}{\sin 2x}

=\dfrac{1+\cos \theta}{\sin \theta} \quad\checkmark

------

For another answer, let's use the hint on this one, which was to write

1=\csc^2 \theta - \cot^2 \theta

That's a good hint; first let's verify if it's true.

\sin^2 \theta + \cos^2 \theta = 1

\sin^2 \theta = 1 - \cos^2 \theta

1 = \dfrac{1}{\sin ^2 \theta} - \dfrac{\cos ^2 \theta}{\sin ^2 \theta}

1 = \csc^2 \theta - \cot^2 \theta \quad\checkmark

Now,

\dfrac{\cot \theta + \csc \theta - 1}{\cot \theta - \csc \theta +1}

= \dfrac{\cot \theta + \csc \theta - (\csc^2 \theta - \cot^2 \theta)}{\cot \theta - \csc \theta +1}

= \dfrac{\cot \theta + \csc \theta +(\cot^2 \theta - \csc^2 \theta)}{\cot \theta - \csc \theta +1}

= \dfrac{\cot \theta + \csc \theta +(\cot \theta - \csc \theta)(\cot \theta + \csc \theta)}{\cot \theta - \csc \theta +1}

= \dfrac{(\cot \theta + \csc \theta)(1+ \cot \theta - \csc \theta)}{\cot \theta - \csc \theta +1}

=\cot \theta + \csc \theta

=\dfrac{ \cos \theta}{\sin \theta}+ \dfrac{1}{\sin \theta}

=\dfrac{1+ \cos \theta}{\sin \theta} \quad\checkmark

You might be interested in
HELP I NEED HELP ASAP
Elanso [62]
I think c) 9 but I’m not too sure
7 0
3 years ago
Perfume is sold in two different sizes of bottle. The 80ml bottle is priced at £55. The 50ml bottle is usually priced at £45, bu
Nadya [2.5K]
1ml of 80ml bottle: 55/80 = 0.6875 pence

1ml of 50ml bottle: 45/50 = 0.9 pence

If no special offer the first bottle is a better value for money.

Since special offer though, you'd be buying;

50ml bottle £45 + another 50ml £22.5 = £67.5 in

which case 1ml would cost;

67.5/100 = 0.675 pence. Hence buying 2x50ml

bottle would be a better value.


8 0
4 years ago
I need help asap im timed
Iteru [2.4K]

Answer:-

<em>Refer</em><em> </em><em>to</em><em> </em><em>attachment</em><em> </em><em>for</em><em> </em><em>the</em><em> </em><em>required</em><em> </em><em>solution</em>.

8 0
3 years ago
Read 2 more answers
Find the 14th term of the geometric sequence 2, 4, 8,
Papessa [141]

Answer:

16384

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A design on the front of a marketing brochure calls for a triangle with a base that is 7 centimeters less than the height. If th
Rainbow [258]
Notice the picture below,
solve for "h" to see what the height of it is

what's the base? well, b = h - 7

8 0
3 years ago
Other questions:
  • Every batch of Lucian's famous chocolate chip cookies takes 9 oz. of chocolate chips. For the school bake sale, he decided to ma
    6·2 answers
  • What does y stand for in y=mx+b
    7·1 answer
  • One card is dealt from a 52 card deck. Find the probability that the dealt card is a 4 or a black 7
    7·2 answers
  • Determine the intercepts of the line.<br> y<br> =<br> 11<br> x<br> +<br> 6
    10·1 answer
  • Please help :)) BRAINIEST
    9·1 answer
  • PLEASE ANSWER ASAP FOR BRAINLEST DUE at 11:59 AND CAN NOT BE LATE PLZ HELP OMG PLZ HELPPPPPPPPPPPPPp GURL IM DYING RN PLZ HURRYY
    11·1 answer
  • Use the Pythagorean identity. (x2 - y²)2 + (2xy)2 = (x2 + y2)2, to create a Pythagorean triple.
    9·1 answer
  • 0 1 2 3 4 5 is an example of what set​
    10·2 answers
  • If H is the center of the circle, find mGJI A 117.33 B 222.57 C 242.67 D 256.56
    10·2 answers
  • Which one is the correct answer?? I’m not getting any of the solutions provided, please help
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!