Question

1+ sin 2 q=3sinq cosq,prove that tanq=1 or 1/2

Answer 1

1+sin²q=3sinqcosq
Dividing both sides by cos²q, we get
1/cos²q+sin²q/cos²q=3sinqcosq/cos²q
or, sec²q+tan²q=3tanq
or, 1+tan²q+tan²q=3tanq
or, 1+2tan²q=3tanq
or, 2tan²q-3tanq+1=0
or, 2tan²q-2tanq-tanq+1=0
or, 2tanq(tanq-1)-1(tanq-1)=0
or, (tanq-1)(2tanq-1)=0
either, tanq-1=0
or, tanq=1
Or, 2tanq-1=0
or, 2tanq=1
or, tanq=1/2
∴, tanq=1 or 1/2

Answer 2

Answer:

Hence proved

see the above attacment