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CBSE Class 10 Answered

if tan^2theta = 1+2tan^2a then prove that 2sin^2theta=1+sin^2a
Asked by vans75a | 07 Sep, 2015, 07:37: PM
answered-by-expert Expert Answer

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

Answered by | 09 Sep, 2015, 06:08: PM

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