if 1+sin2theta=3 sintheta cos theta then show that tantheta=1 or 1/2
 

Asked by Rahul Meena | 13th Sep, 2014, 06:13: PM

Expert Answer:

C o n s i d e r space t h e space e q u a t i o n comma 1 plus sin squared theta equals 3 sin theta cos theta W e space n e e d space t o space p r o v e space t h a t space tan theta equals 1 space o r space 1 half 1 plus sin squared theta equals 3 sin theta cos theta D i v i d e space t h e space d e n o m i n a t o r space b y space cos squared theta comma space w e space h a v e comma fraction numerator 1 plus sin squared theta over denominator cos squared theta end fraction equals 3 tan theta rightwards double arrow fraction numerator 1 over denominator cos squared theta end fraction plus fraction numerator sin squared theta over denominator cos squared theta end fraction equals 3 tan theta rightwards double arrow s e c squared theta plus tan squared theta equals 3 tan theta rightwards double arrow 1 plus tan squared theta plus tan squared theta equals 3 tan theta rightwards double arrow 2 tan squared theta minus 3 tan theta plus 1 equals 0 rightwards double arrow tan theta equals fraction numerator 3 plus-or-minus square root of open parentheses minus 3 close parentheses squared minus 4 cross times 2 end root over denominator 2 cross times 2 end fraction rightwards double arrow tan theta equals fraction numerator 3 plus-or-minus square root of 9 minus 8 end root over denominator 4 end fraction rightwards double arrow tan theta equals fraction numerator 3 plus-or-minus 1 over denominator 4 end fraction rightwards double arrow tan theta equals 1 space o r space tan theta equals 1 half

Answered by Vimala Ramamurthy | 13th Sep, 2014, 08:09: PM