Question

If tan 3 x= sin 45.cos 45+ sin 30 ,then find x

Answer 1

RHS:
sin45.cos45+sin30
=1|√2.1|√2 + 1|2
= 1|2+1|2
=2|2
=1


now,
tan 3x = 1
but tan 45° = 1
therefore,
tan 3x = tan 45
means 3x = 45
& x=45÷3
hence x= 15

Answer 2

tan3x = sin45°cos45° + sin30°
         = (1/√2)×(1/√2) + 1/2 
         = 1/2 + 1/2
         = 1
tan 45° = 1
so, 3x = 45
⇒x = 15°