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secondary 4 | A Maths
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genevieve
Genevieve

secondary 4 chevron_right A Maths chevron_right Singapore

Very confused on how to solve qn 7 and 12. Would appreciate detailed worked solution asap. Thanks!!

Date Posted: 4 years ago
Views: 541
Eric Nicholas K
Eric Nicholas K
4 years ago
Q12 is not easy and I will look at them by 4 am.
snell
Snell
4 years ago
(ii)
cot π/8 = cosec π/4 + cot π/4
= √2 + 1

cot π/12 = cosec π/6 + cot π/6
= 2/√3 + 1/√3
= 3/√3
= √3

.
snell
Snell
4 years ago
(i)
see x on left & and see x/2 on right ,
recall double angle identities


cosec x + cot x
= 1/sin 2(x/2) + 1/tan 2(x/2)
= 1/[ 2 sin (x/2) cos (x/2)] +
[ 1 - tan² (x/2) ] /[ 2 tan (x/2) ]

= [ 1/cos² (x/2) ]/[ 2 sin (x/2) cos (x/2)]/[ cos² (x/2) ] +
[ 1 - tan² (x/2) ] /[ 2 tan (x/2) ]

= [ sec² (x/2) ]/[ 2 tan (x/2) ] +
[ 1 - tan² (x/2) ] /[ 2 tan (x/2) ]

= [ 1 + tan² (x/2) ]/[ 2 tan (x/2) ] +
[ 1 - tan² (x/2) ] /[ 2 tan (x/2) ]

= 2/[ 2 tan (x/2) ]

= 1/[tan (x/2) ]

= cot (x/2) (proved)

.
snell
Snell
4 years ago
(iii)

from (i) ,
cosec x = cot x/2 - cot x

likewise ,
cosec 2x = cot x - cot 2x ; &

cosec 4x = cot 2x - cot 4x


hence ,

cosec x + cosec 2x + cosec 4x

= cot x/2 - cot x + cot x - cot 2x + cot 2x - cot 4x

= cot x/2 - cot 4x

.
snell
Snell
4 years ago
(iv)
from (iii) ,

cosec 4π/15 + cosec 8π/15 + cosec 16π/15 + cosec 32π/15

= cot 4π/30 - cot 32π/15
= cot 2π/15 - cot 32π/15
= cot 2π/15 - cot (2π + 2π/15)
= cot 2π/15 - cot 2π/15
= 0

*note: 2π + 2π/15 is in 1st quad.

cot (2π + 2π/15) = cot 2π/15

.
.
.
genevieve
Genevieve
4 years ago
Thanks!!

See 7 Answers

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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Good afternoon Cheryl! Here are my workings for Q7c.
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Good afternoon Cheryl! Here are my workings for Q7d.
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Good afternoon Cheryl! Here are my workings for Q7e.
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Good afternoon Cheryl! Here are my workings for Q7f. I will look at Q12 when I have more time.
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Good evening Cheryl! Here are my workings for Q12. Ignore my irrelevant workings in the "first quadrant".
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
1st
Good morning Cheryl! Here are my workings for Q7a. I will do the remaining questions when I have more time, by 4 am.
genevieve
Genevieve
4 years ago
Thank you!!
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Good evening Cheryl! Here are my workings for Q7b.