Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 8

EASY

AS and A Level

IMPORTANT

Earn 100

Given that $\tan A = t$ and that $\tan (A - B) = 2$ , find $\tan B$ in terms of $t .$

Important Questions on Trigonometry

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 9

If

\cos (A - B) = 3 \cos (A + B)

, then the exact value of

\tan A \tan B = \frac{1}{k}

. Hence,

k =

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 10

Given that

8 + {cosec}^{2} θ = 6 \cot θ

, find the value of

\tan θ

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 10

If

\tan θ = \frac{1}{3}

. Find the exact value of

\tan (θ + 45 °)

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 11

Given that

x

is acute and that

2 \sec^{2} x + 7 \tan x = 17

, If the exact value of

\tan x

is

\frac{a}{b}

, where

a

, and

b

are co-prime numbers then

a + b =

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 11

Given that

x

is acute and that

2 \sec^{2} x + 7 \tan x = 17

, find the exact value of

\tan x

. Hence find the exact value of

\tan (225 ° - x)

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 12

Show that the equation

\sin (x + 30 °) = 5 \cos (x - 60 °)

can be written in the form

\cot x = - \sqrt{3}

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 12

Solve each equation for $0 ° ⩽ x ⩽ 360 °$ , $\cos (x + 30 °) = 2 \sin x$ .[Use $\tan^{- 1} (\frac{\sqrt{3}}{5}) = 19.1 °$ ]

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3B>Q 13

Solve the equation $\cos (x + 30 °) = 2 \sin x$ for $0 ° ⩽ x ⩽ 360 °$