Question

If root 2 tan theta = 3 sin theta then find value of sin2 theta - cos 2 theta

Answer 1

HELLO DEAR,



√2tan∅ = 3sin∅


sin∅/cos∅ = 3sin∅/√2


1/cos∅ = 3/√2


cos∅ = √2/3


cos²∅ = 2/9------(1)


NOW,


sin²∅ = 1 - cos²∅

sin²∅ = 1 - 2/9

sin²∅ = (9 - 2)/9

sin²∅ = 7/9---------(2)



now,

subtracting from----(2) & -----(1)


we get,

sin²∅ - cos²∅

=> 7/9 - 2/9

=> (7 - 2)/9

=> 5/9.


I HOPE ITS HELP YOU DEAR,
THANKS