If 1 + (sin α) ^ 2 = 3sin α cos α, find Tan α

1+(sinα)^2=3sinαcosα
Substituting 1 = (sin α) ^ 2 + (COS α) ^ 2 into the original equation, 2 (sin α) ^ 2 + (COS α) ^ 2 = 3sin α cos α
Divide both sides by (COS α) ^ 2
2(tanα)^2-3tanα+1=0
=> (2tanα-1)(tanα-1)=0
Tan α = 1 / 2 or tan α = 1

Tan α = 3. Find 3sin ^ 2 α - sin α cos α + 2

tanα=3
sinα/cosα=3
sin^2α/cos^2α=9
(1-cos^2α)/cos^2α=9
1/cos^2α-1=9
cos^2α=1/10
3sinα^2-sinαcosα+2
=cos^2α(3tan^2α-tanα)+2
=1/10*(3*3^2-3) + 2
=12/5+2
=22/5

If 1 + (sin α) ^ 2 = 3sin α cos α, find Tan α

If 1 + (sin α) ^ 2 = 3sin α cos α, find Tan α

Tan α = 3. Find 3sin ^ 2 α - sin α cos α + 2

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