(iv)√
3
2π
3nπ+(− 1 )nπ
3π
62 nπ±π
6(v)1
√
2π
4nπ+(− 1 )nπ
4π
42 nπ±π
4(vi) −1
√
2−π
4nπ+(− 1 )n+^1π
43 π
42 nπ±3 π
4
wherenis an integerB.
tan−^1 x 01√
3 − 1 −1
√
3PV 0π
4π
3−π
4−π
6
GS nπ nπ+π
4nπ+π
3nπ−π
4nπ−π
66.3.6 The Pythagorean identities – cos^2 Ysin
2
= 1
A.You may obtain different forms of the answers – consider it a further exercise to check
their equivalence to the following!
(i) (a) sinθ (b) cotθ (c) tan^2 θ
(ii) (a) cosθ (b) cosecθcotθ (c) secθtanθ(iii) (a) secθ (b) sinθcosθ (c) cosθcotθ
B. (i)
x^2
a^2+y^2
b^2= 1 (ii) y=bx
√
a^2 −x^2C. (i)
√
21
5,2
√
21(ii)2√
42
13,1
2√
42(iii)24
25,7
24D.5, 53.13°
6.3.7 Compound angle formulae
B. (i)
1
4(ii)√
2 (√
3 − 1 )
4(iii) 2−√
3(iv) −√
2 (√
3 + 1 )
4(v) −( 2 +√
3 ) (vi)√
2 (√
3 − 1 )
4C. (i)
√
( 2 −√
2 )
2(ii)√
2 +√
2
2(iii)√
6 ( 2 −√
2 )
6