F.4 Add.Maths既題目..Trigonometry....(10分!!)急.....

Answer ALL Questions.

Prove the following identities.

1)sec²θcosec²θ = sec²θ+cosec²θ

2)(Asec x + Btan x)² - (Atan x + Bsec x)² = A² - B²

3)sinB+sinAcos(A+B) / cosB-sinAsin(A+B) = tan(A+B)

4)cot(A+B) = cotAcotB-1 / cotA+cotB

5)If A+B+C = 180', show that
cosA = sinBsinC - cosBcosC

6)Prove that in (三角形符號)ABC,
(a)cot A/2 = tan(B/2+C/2) by using the identity cot x = tan(90-x)
(b)Hence show that cotA/2 + cot B/2 +cotC/2 = cot A/2cotB/2cotC/2.