Archive
9th of September 2015
Mathematics
Q:

if tan^2theta = 1+2tan^2a then prove that 2sin^2theta=1+sin^2a

Naina Chauhan - CBSE - Class X

Monday, September 07, 2015 at 19:37:PM

A:

G i v e n space t h a t space tan squared theta equals 1 plus 2 tan squared a A d d i n g space 1 space t o space b o t h space t h e space s i d e s space o f space t h e space e q u a t i o n comma space w e space h a v e comma 1 plus t a n squared theta equals 1 plus 1 plus 2 t a n squared a rightwards double arrow 1 plus t a n squared theta equals 2 plus 2 t a n squared a rightwards double arrow s e c squared theta equals 2 plus 2 t a n squared a rightwards double arrow s e c squared theta equals 2 open parentheses 1 plus tan squared a close parentheses rightwards double arrow s e c squared theta equals 2 s e c squared a rightwards double arrow fraction numerator 1 over denominator s e c squared theta end fraction equals fraction numerator 1 over denominator 2 s e c squared a end fraction rightwards double arrow cos squared theta equals 1 half cos squared a rightwards double arrow 1 minus c o s squared theta equals 1 minus 1 half c o s squared a rightwards double arrow 1 minus c o s squared theta equals 1 minus 1 half open parentheses 1 minus sin squared a close parentheses rightwards double arrow sin squared theta equals 1 minus 1 half plus fraction numerator sin squared a over denominator 2 end fraction rightwards double arrow s i n squared theta equals 1 half plus fraction numerator s i n squared a over denominator 2 end fraction rightwards double arrow s i n squared theta equals fraction numerator 1 plus s i n squared a over denominator 2 end fraction rightwards double arrow 2 s i n squared theta equals 1 plus s i n squared a

Wednesday, September 09, 2015 at 18:08:PM