“Everything you’ve ever wanted is on the other side of fear.” — George Addair

Exercise 3.3 Question 2 \( 2\sin^2 \frac{\pi}{6} + \cosec^2 \frac{7\pi}{6} \cos^2 \frac{\pi}{3} = \frac{3}{2}\)

Exercise 3.3 Question 4 \(2\sin^2 \frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{\pi}{3}=10\)

Derivation of identity for sin(A+B) using example of sin75°

Value of sin75° using sin(A+B) identity

Exercise 3.3 Question 5 Find the value of:

(i) sin 75°

(ii) tan 15°

Derivation of

\(\sin(A+B) = \sin A \cos B + \cos A \sin B\)

\(\sin(A-B) = \sin A \cos B – \cos A \sin B\)

\(\cos(A+B) = \cos A \cos B – \sin A \sin B\)

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

\(\tan(A+B) = \frac{\tan A + \tan B}{1-\tan A \tan B}\)

\(\tan(A-B) = \frac{\tan A – \tan B}{1+\tan A \tan B}\)

Example 13 Prove that \( \frac{\sin(x+y)}{\sin(x-y)} = \frac{\tan x + \tan y}{\tan x – \tan y}\)