is there any short trick to solve the problem involvingtan(@).tan(2@).tan(3@)....tan(n@).also derive.PLz

Hello Sawan ..!

Are you sure ...the arguments are always in the AP form ..like   @ , 2@ , 3@ ....n@   or it is random .. like 43 , 46 , 76 ..etc

If it is random ....then this kind of problem has only one trick ..Either the last term will be the complemet of the first term ..

Like tan(n@) = cot(@)

So you substitute at the place of tan(n@) and the first term will be cancelled out ..

similarly every term will be cancelled out ..and the middle term ..(may be) will be tan45 ..which it self is 1 hence the option will be 1 ..

Else ...you have to use tan ( A + B + C + D .............) expansion which not an easy tast ..

And remember if this kind of question is asked in any competive exams ..then be sure they can be easily solved by using small tricks...like the one i have told you above..

Hope it is clear to you now :)

Regards

Yagya

Askiitian_expert