Quick questions on Trigonometric identities: N(A)-Level Additional Mathematics

If you know one ratio and the quadrant, the Pythagorean identity gives the others. Solve for the square, take the square root, and choose the sign from the quadrant. The quotient identity then gives tangent.

To prove an identity, work on one side only (usually the more complicated one) and use the two identities, plus ordinary algebra, until it matches the other side. Do not move terms across the equals sign as if solving an equation; instead transform one side step by step. Writing $\tan\theta$ as $\dfrac{\sin\theta}{\cos\theta}$ early often unlocks the proof.

Given $\cos\theta = 0.8$ and $\theta$ acute, find $\sin\theta$. [2 marks]

Simplify $1 - \cos^2\theta$. [1 mark]

Prove that $\tan\theta\,\cos\theta = \sin\theta$. [2 marks]