Introduction to Trigonometry question bank (Maths)

Consider $\triangle ACB$,right-angled at $C$,in which $AB = 29$ units,$BC = 21$ units and $\angle ABC = \theta$. Determine the values of:
$(i)$ $\cos^2 \theta + \sin^2 \theta$
$(ii)$ $\cos^2 \theta - \sin^2 \theta$

In $\triangle OPQ$,right-angled at $P$,$OP = 7\, cm$ and $OQ - PQ = 1\, cm$. Determine the values of $\sin Q$ and $\cos Q$.