Question and Answers Forum

All Questions   Topic List

GeometryQuestion and Answers: Page 87

Question Number 52663    Answers: 2   Comments: 1

Question Number 52539    Answers: 2   Comments: 0

Question Number 52533    Answers: 0   Comments: 5

Question Number 52523    Answers: 0   Comments: 12

Question Number 52468    Answers: 2   Comments: 4

Question Number 52433    Answers: 0   Comments: 4

Question Number 52428    Answers: 0   Comments: 7

Question Number 52426    Answers: 2   Comments: 1

Question Number 52409    Answers: 1   Comments: 1

Question Number 52360    Answers: 1   Comments: 1

Question Number 52321    Answers: 0   Comments: 0

Question Number 52261    Answers: 0   Comments: 9

Question Number 52198    Answers: 2   Comments: 0

Question Number 52182    Answers: 0   Comments: 1

Question Number 52190    Answers: 2   Comments: 3

Question Number 52129    Answers: 1   Comments: 5

Question Number 52061    Answers: 2   Comments: 3

Question Number 52052    Answers: 0   Comments: 1

Question Number 52016    Answers: 1   Comments: 1

Question Number 52012    Answers: 0   Comments: 2

Question Number 51973    Answers: 0   Comments: 1

Question Number 51942    Answers: 1   Comments: 5

Question Number 51911    Answers: 0   Comments: 2

Question Number 51905    Answers: 2   Comments: 0

If p = cos θ + i sinθ and q = cos φ + i sin φ Show that: (i) ((p − q)/(p + q)) = i tan (((θ − φ)/2)) (ii) (((p + q)(pq − 1))/((p − q)(pq + 1))) = ((sin θ + sin φ)/(sin θ − sin φ))

$$\mathrm{If}\:\:\:\mathrm{p}\:\:=\:\:\mathrm{cos}\:\theta\:+\:\mathrm{i}\:\mathrm{sin}\theta\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\mathrm{q}\:\:=\:\:\mathrm{cos}\:\phi\:+\:\mathrm{i}\:\mathrm{sin}\:\phi \\ $$$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\:\:\frac{\mathrm{p}\:−\:\mathrm{q}}{\mathrm{p}\:+\:\mathrm{q}}\:\:=\:\:\mathrm{i}\:\mathrm{tan}\:\left(\frac{\theta\:−\:\phi}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{ii}\right)\:\:\:\frac{\left(\mathrm{p}\:+\:\mathrm{q}\right)\left(\mathrm{pq}\:−\:\mathrm{1}\right)}{\left(\mathrm{p}\:−\:\mathrm{q}\right)\left(\mathrm{pq}\:+\:\mathrm{1}\right)}\:\:=\:\:\frac{\mathrm{sin}\:\theta\:+\:\mathrm{sin}\:\phi}{\mathrm{sin}\:\theta\:−\:\mathrm{sin}\:\phi} \\ $$

Question Number 51884    Answers: 1   Comments: 4

Question Number 51849    Answers: 3   Comments: 3

  Pg 82      Pg 83      Pg 84      Pg 85      Pg 86      Pg 87      Pg 88      Pg 89      Pg 90      Pg 91   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com