How can this be solved?

3tan^2(x) + 13tan(x) - 10

2 Answers
Aug 1, 2018

Note:To complete equation we have to take,
3tan^2x+13tanx-10=0

x={kpi+arctan(2/3) ,kin ZZ}uu{kpi-arctan(5) ,k in ZZ}

Explanation:

Here ,

3tan^2x+13tanx-10=0

=>3tan^2x-2tanx+15tanx-10=0

=>tanx(3tanx-2)+5(3tanx-2)=0

=>(3tanx-2)(tanx+5)=0

=>3tanx-2=0 or tanx+5=0

=>tanx=2/3 or tanx=-5

(i)tanx=2/3=>x=kpi+arctan(2/3) ,kin ZZ

(ii)tanx=-5=>x=kpi+arctan(-5),kinZZ

i.e. x=kpi-arctan(5) ,k in ZZ

Note:To complete equation we have to take,

3tan^2x+13tanx-10=0

Aug 1, 2018

tanx=2/3

x=0.588+npi where n is an integer


tanx=-5

x=1.77 +npi where n is an integer

Explanation:

3tan^2x+13tanx-10

Think of tanx as y

So, 3tan^2x+13tanx-10 becomes 3y^2+13y-10

Then, using the quadratic formula,

y=(-13+-sqrt(13^2-4(3)(-10)))/(2times3)

y=(-13+-sqrt289)/6

y=(-13+-17)/6

y=(-13+17)/6 and y=(-13-17)/6

y=2/3 or y=-5

Since y=tanx, then

tanx=2/3 or tanx=-5

tanx=2/3

x=0.588+npi where n is an integer


tanx=-5

x=1.77 +npi where n is an integer