Cambridge Additional Mathematics

248 Trigonometric functions (Chapter 9)

3 Simplify:

a 3 tanx¡

sinx

cosx

b

sin^2 x

cos^2 x

c tanxcosx

d

sinx

tanx

e 3 sinx+ 2 cosxtanx f

2 tanx

sinx

g tanxcotx h sinxcosecx i

j sinxcotx k

cotx

cosecx

l

2 sinxcotx+ 3 cosx

cotx

4 Expand and simplify if possible:

a (1 + sinμ)^2 b (sin®¡2)^2 c (tan®¡1)^2

d (sin®+ cos®)^2 e (sin ̄¡cos ̄)^2 f ¡(2¡cos®)^2

5 Simplify:

a 1 ¡sec^2 ̄ b

tan^2 μ(cot^2 μ+1)

tan^2 μ+1

c cos^2 ®(sec^2 ®¡1) d (sinx+ tanx)(sinx¡tanx)

e (2 sinμ+ 3 cosμ)^2 + (3 sinμ¡2 cosμ)^2 f (1 + cosecμ)(sinμ¡sin^2 μ)

g secA¡sinAtanA¡cosA

FACTORISING TRIGONOMETRIC EXPRESSIONS

Example 14 Self Tutor

Factorise:

a cos^2 ®¡sin^2 ® b tan^2 μ¡3 tanμ+2

a cos^2 ®¡sin^2 ®

= (cos®+ sin®)(cos®¡sin®) fcompare with a^2 ¡b^2 =(a+b)(a¡b)g

b tan^2 μ¡3 tanμ+2

= (tanμ¡2)(tanμ¡1) fcompare with x^2 ¡ 3 x+2=(x¡2)(x¡1)g

EXERCISE 9F.2

1 Factorise:

a 1 ¡sin^2 μ b sin^2 ®¡cos^2 ®

c tan^2 ®¡ 1 d 2 sin^2 ̄¡sin ̄

e 2 cosÁ+ 3 cos^2 Á f 3 sin^2 μ¡6 sinμ

g tan^2 μ+ 5 tanμ+6 h 2 cos^2 μ+ 7 cosμ+3

i 6 cos^2 ®¡cos®¡ 1 j 3 tan^2 ®¡2 tan®

k sec^2 ̄¡cosec^2 ̄ l 2 cot^2 x¡3 cotx+1

m 2 sin^2 x+ 7 sinxcosx+ 3 cos^2 x

secxcotx

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\248CamAdd_09.cdr Wednesday, 15 January 2014 10:43:26 AM BRIAN