Which one of the following options is correct ?

Options

A. `sin^(2)30^(@),sin^(2)45^(@),sin^(2)60^(@)`, are in GP
B. `cos^(2)30^(@),cos^(2)45^(@),cos^(2)60^(@)` are in GP
C. `cot^(2)30^(@),cot^(2)45^(@),cot^(2)60^(@)` are in GP
D. `tan^(2)30^(@),tan^(2)45^(@),tan^(2)60^(@)` are in GP

Answer

D

Explanation

Three numbers a, b and c will be in G.P. if `b^(2)=ac.`
Only option (d) i.e. `tan^(2)30^(@),tan^(2)45^(@)" and "tan^(2)60^(@)` are ub GP.
`because" "tan^(2)30^(@)=(1)/(3)`
`tan^(2)45^(@)=1`
and `tan^(2)60^(@)=3`
`:." "tan^(2)30^(@),tan^(2)45^(@)" and "tan^(2)60^(@)` are in G.P.