Question

if cos beta is geometric mean between sin alpha and cos alpha where 0<alpha,beta<pi/2 then cos 2beta equals

Answer 1

Dear Student,
$$\begin{gathered} Given, \\ \cos \beta isthegeometricmeanof\sin \alpha and\cos \alpha . \\ i.e \\ {\cos }^2\beta =\sin \alpha .\cos \alpha \\ 2{\cos }^2\beta =2\sin \alpha .\cos \alpha \\ 1+\cos 2\beta =\sin 2\alpha \\ \cos 2\beta =\sin 2\alpha -1. \end{gathered}$$
Regards.