trig question (1 Viewer)

[martin310015]

having trouble with this questions, how would i start them ......

1.using double angle formula for tan@, find tan22/2degree in simplest surd form.

2.if tan@=k tan# , show that

(k-1)sin(@+#)=(k+1)sin(@-#)

thanx

 

[Xayma]

Just to give you a start with number 1.

tan 2@=45 degrees
tan 2@= 2tan @/(1-tan² @)
but tan 2@=1
therefore
1=2tan @/(1-tan² @)

Work from there just some rearranging etc.

 

[nike33]

for the second one, convet to sin / cos then use sum / product rules

 

[martin310015]

Originally posted by Xayma
Just to give you a start with number 1.

tan 2@=45 degrees
tan 2@= 2tan @/(1-tan² @)
but tan 2@=1
therefore
1=2tan @/(1-tan² @)

Work from there just some rearranging etc.

i managed to do this one.

Originally posted by nike33
for the second one, convet to sin / cos then use sum / product rules

but for this one im still confused......

 

[Xayma]

(k-1)sin(@+#)
=(k-1)(sin@cos#+cos@sin#)
=ksin@cos#-sin@cos#+kcos@sin#-cos@sin#
=ksin@cos#-tan@cos@cos#+ktan#cos@cos#-cos@sin#
=ksin@cos#-ktan#cos@cos#+tan@cos@cos#-cos@sin#
=ksin@cos#-ksin#cos@+sin@cos#-cos@sin#
=(k+1)sin@cos#-(k+1)sin#cos@
=(k+1)(sin@cos#-sin#cos@)
=(k+1)sin(@-#)

 

[nike33]

now can you find a 3 line proof?

 

[Heinz]

Let me give it a go

tan@=k tan#
sin@/cos@ = ksin#/cos#
sin@cos# = ksin#cos@

(k-1)sin(@+#)
= (k-1)(sin@cos# + cos@sin#)
= (k-1)(ksin#cos@ + cos@sin#)
= (k-1)(k+1)(sin#cos@)
= (k+1)(ksin#cos@-sin#cos@)
= (k+1)(sin@cos# -sin#cos@)
= (k+1)(sin(@-#)

hmm.... that isnt 3 lines.

 

[nike33]

@ and # are evil anyhow (A=@, B=#)

2sinAcosB = 2kcosAsinB
sin(A+B) + sin(A-B) = ksin(A+B) - ksin(A-B)
(k-1)sin(A+B) = (k+1)sin(A-B)

 

[nike33]

are product / sums on the 3 unit sylabus? or only 4unit? and in a 2u exam, we had a trig qn, the given answer was 11-12 lines (out of 5 marks) anyhow i did it in 3-4 lines using product/sum and got 0 lol.. i would do something but 2u doesnt count so meh

 

[Heinz]

Originally posted by nike33
are product / sums on the 3 unit sylabus? or only 4unit? and in a 2u exam, we had a trig qn, the given answer was 11-12 lines (out of 5 marks) anyhow i did it in 3-4 lines using product/sum and got 0 lol.. i would do something but 2u doesnt count so meh

Nice solution. Sum and products are part of 3unit but no one bothers to learn them (unless you do 4unit)