Prove that, if \(\tan\theta\tan(\theta+\alpha)=k\), then \[(k+1)\cos(2\theta+\alpha)=(1-k)\cos\alpha.\]

Solve the equation \[\tan\theta\tan(\theta+\pi/3)=2.\]

Discuss the equation \[\tan\theta\tan(\theta+\alpha)+1=0.\]

Can you think of any formulae relating \(\sin, \tan\) and \(\cos\)?

Can we expand \(\cos A\cos B\)? Or \(\sin A \sin B\)?

If we can’t do the first part, can we still do the second and third parts (using the result from the first part)?