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SEAMO 2027 - Paper F - SET 05 - Self-study Question 19

SEAMO · SEAMO 2027 - Paper F - SET 05 - Self-study

Question 19

If $x=\sin\alpha$, $y=\sin\beta$ and $z=\sin(\alpha+\beta)$, find $\cos(\alpha+\beta)$.

Domain for this self-study question: x and y are both nonzero. Compare the options as identities valid throughout this domain. The source omits this restriction although its options contain denominators x or xy.
  1. $\frac{x^2+y^2+z^2}{2xy}$
  2. $\frac{x^2+y^2-z^2}{x}$
  3. $\frac{z^2-x^2-y^2}{2xy}$
  4. $\frac{z^2-x^2-y^2}{xy}$
  5. $\frac{z^2+x^2-y^2}{xy}$