Question

Trigonometic Equations and Inequalities.
Solve the following equations
For what a does the equation $1+si{n}^{2}ax=cosx$ possess a unique solution?

Answer 1

cosx varies from -1 to 1

$sin(\alpha \ast x{)}^2$> or equal to 0 always therefore

1+$sin(\alpha \ast x{)}^2$ is always greater or equal to 1

therefore cosx=1=$sin(\alpha \ast x{)}^2$ has unique solution

only when $\alpha$=0