tan 48 tan23tan 42 tan 67=1 solve it and tell me y we dont change all the four tan value as tan (90-a)=cot a

Dear Student,

$$\begin{gathered} \tan 48\tan 23\tan 42\tan 67 \\ =\tan \left[90-42\right]\tan \left(90-67\right)\tan 42\tan 67 \\ =\cot 42\times \cot 67\times \tan 42\tan 67 \\ =\frac{1}{\tan 42\tan 67}\times \tan 42\tan 67 \\ =1 \end{gathered}$$

as we wanted to prove the result as 1 hence we want both cot and tan to be cancelled. that's why only two of the expressions are converted to cot,so that those can be cancelled out by remaining tan expressions.

Regards,