Question

if tan(thetha)=a/b
find the value of asin2thetha + b cos2thetha

Answer 1

hope this helps you..........

Answer 2

tanthetha=a/b
then from Pythagoras theorem
hypotenuse square=opp square+adj square
hypotenuse square=asquare+b square
hypotenuse =√asquare+bsquare
so sintheta=a/√asquare+bsquare,costhetha=b/√a square+bsquare
asin2 thetha=a(2sinthethacosthetha)
=a(2ab/asquare+bsquare)
bcos2thetha=b(2cossquaretheta-1)
=b(2(b/asquare+bsquare)-1)
we get answer by adding 1 and 2