I know that $$\cos \theta = \sin (\frac{\pi}{2}-\theta)$$ $$\sin \theta = \cos (\frac{\pi}{2}-\theta)$$
I am not sure if it was addition or subtraction. I forgot those formula. I was trying to derive it.
$$\cos^2 (\theta)+\sin^2 (\theta)=1$$ $$\cos^2(\theta)=-\sin^2(\theta)+\sin^2(\frac{\pi}{2})$$ $$\cos^2(\theta)=\sin^2(\frac{\pi}{2}-\theta)$$
But, I know that $$-\sin^2(\theta)+\sin^2(\frac{\pi}{2})\not= \sin^2(\frac{\pi}{2}-\theta)$$
I saw some weird equations also.
$$2\cos^2 \frac{\theta}{2} = 1-\cos \theta$$ $$2\sin^2 \frac{\theta}{2} = 1-\cos \theta$$
Could you suggest me a book (PDF) which I could use for practicing double/half angle formula? Which book should I follow for trigonometry?
Regarding your book recommendation, here is one: