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
S_A_V [24]
2 years ago
11

Please help, performance task: trigonometric identities

Mathematics
2 answers:
ss7ja [257]2 years ago
6 0

Answer:

<u>Trigonometric Identities used:</u>

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

\sec \theta \equiv \dfrac{1}{\cos \theta}

\cot \theta  \equiv \dfrac{1}{\tan \theta}

\sec^2 \theta \equiv 1 + \tan^2 \theta

\sin(\theta)=\cos \left(\dfrac{\pi}{2}-\theta\right)

<u>Part (a)</u>

   (1+ \cos(x))(1-\cos(x))

=1-\cos(x)+\cos(x)-\cos^2(x)

=1-\cos^2(x)

= \sin^2(x)

<u>Part (b)</u>

   \dfrac{1}{\cot^2(x)}-\dfrac{1}{\cos^2(x)}

=\tan^2(x)-\sec^2(x)

=\tan^2(x)-(1 + \tan^2(x))

=\tan^2(x)-1 - \tan^2(x)

=-1

<u>Part (c)</u>

   \sec^2\left(\dfrac{ \pi }{2}-x\right) \left[\sin^2(x)-\sin^4(x) \right]

=\dfrac{1}{\cos^2\left(\dfrac{ \pi }{2}-x\right)} \left[\sin^2(x)-\sin^4(x) \right]

=\dfrac{1}{\sin^2(x)} \left[\sin^2(x)-\sin^4(x) \right]

= \dfrac{\sin^2(x)-\sin^4(x)}{\sin^2(x)}

= \dfrac{\sin^2(x)}{\sin^2(x)} - \dfrac{\sin^4(x)}{\sin^2(x)}

= \dfrac{\sin^2(x)}{\sin^2(x)} - \dfrac{(\sin^2(x))(\sin^2(x))}{\sin^2(x)}

=1- \sin^2(x)

= \cos^2(x)

kramer2 years ago
6 0

#a

  • (1+cosx)(1-cosx)
  • 1²-cos²x
  • 1-cos²x
  • sin²x

#2

  • 1/cot²x-1/cos²x
  • tan²x-sec²x
  • -1

#c

  • sec²(90-x)[sin²x-sin⁴x]
  • csc²x[sin²x-sin⁴x]
  • 1-sin²x
  • cos²x
You might be interested in
Factor 3x2 - 6x - 9 completely​
Crazy boy [7]
3(x^2-2x-3)
3(x-3)(x+1)
7 0
3 years ago
Read 2 more answers
Please help with this
Archy [21]

Answer:

The transformation is a reflection across the y-axis.

7 0
3 years ago
Read 2 more answers
In a school with 2,000 students a random sample of 120 students were asked which fruit was there favorite. Their responses are s
Sladkaya [172]

2000 / 120 = 16,66

16,66 * 34 = 566,6 ≈ 567

4 0
4 years ago
The scale on a map is 1: 20 000.
Vlada [557]

Answer:

0.54kilometres

Step-by-step explanation:

a)actual distance =2.7*20000

                            =54000cm

                             =0.54kilometres

5 0
3 years ago
Help Julie has the boxes of pens
professor190 [17]

Answer:

A=C+16

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Which digit could be found in the ones place of an odd number?
    10·1 answer
  • Bryan is mapping out essential and non-essential expenses. He owes a car payment of $235 per month for 45 more months. Bryan is
    9·2 answers
  • Each of the triangular faces has an area of 32 m2.
    9·1 answer
  • Help me..............
    13·1 answer
  • A children's roller coaster is limited to riders whose height is at least 30 inches and at most 48 inches. Write two inequalitie
    6·1 answer
  • Help me with this plz, I’m not so smart when it come to math. Math ain’t my strong suit
    6·1 answer
  • What is the measure of an angle that is supplementary to an angle that measures 101°? (Type number only)
    14·1 answer
  • HELP!!!!!A school is having a competition to see who can read the most books in one month (30 days). In the first 5 days, Jake r
    11·1 answer
  • Write each recurring decimal as a fraction in simplest form.<br> 0.286
    7·1 answer
  • What is the value of tan(60°)?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!