Trig

Question 1

How to draw sec x

Answer 1

U shape across y-à is
Half us either side
Full ns in between

Question 2

How to draw cosec x

Answer 2

U after y axis, full u on left hand said

N before y axis, full n on rhs

Question 3

Sec^2 x

Answer 3

1 + tan^2 x

Question 4

Cosec^2 x

Answer 4

1 + cot^2 x

Question 5

Prove that 1 + tan^2 x = sec^2 x

Answer 5

Divide each term by cos^2 x from sin^2 x + cos^2 x = 1, which we know to be true

Question 6

Prove that 1 + cot^2 x = cosec^2 x

Answer 6

Divide each term by sin^2x from sin^2 x + cos^2 x = 1, which we know to be true

Question 7

‘Given that’

Answer 7

• use identities
• sketch graphs
• when deciding if solution is positive or negative, use ordinary graphs, as the sign will be the same as the reciprocal

Question 8

Proof tips

Answer 8

• Look for DOTS
• Simplify side with higher power
• always expand addition formulae

Question 9

tan (A+B)

Answer 9

(tan À + tan B) / (1+ tanAtanB)

Question 10

Prove cos(A-B)

Answer 10

Can use cos(A+B) , then set B and (-B)
• cos(B) = cos(-B) because cos is symmetric
• sin(-B) = -sin(B)

Question 11

Prove tan(A+B)

Answer 11

Sin(A+B) / cos(A+B)

Divide everything by cosAcosB

Question 12

Cos2A

Answer 12

2cos^2A -1

1- 2sin^2A

Question 13

Tan2A

Answer 13

(2tanA) / (1-tan^2 A)

Question 14

Prove double angle formulae

Answer 14

Use addition formulae