CBSE BOARD X, asked by LOLEMOTE, 1 month ago

if sin alpha+beta=1,sin alpha-beta=1/2,alpha,beta belongs to[0, pie/2] then find the value of tan ( alpha+2 beta) × tan( 2alpha+ beta)

Answers

Answered by lokeshnandigam69
17

 </p><p>\huge\orange{ANSWER}

 \sin( \alpha  +  \beta)  = 1 \: and \:  \sin( \alpha  -  \beta )  = 1 \div 2

 \sin( \alpha  +  \beta )  =  \sin(90) and \:  \sin( \alpha  -  \beta ) =  \sin(30)

( \alpha  +  \beta ) = 90 \: and  \: ( \alpha  -  \beta ) = 30

by \: adding

 \alpha  = 60 \:  \beta  = 30

 \tan(2 \alpha  +  \beta )  =  \tan(2 \times 60 + 30)  =  \tan(150)

 \tan(2 \alpha  +  \beta )  =  -  \sqrt{3}  \div 3

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