Question

Find possible value of tan x if cos^2 x +5sin x × cos x =3

Answer 1

Step-by-step explanation:

cos²x+5sinxcosx=3

dividing both sides by cos²x

cos²x/cos²x + 5sinxcosx/cos²x=3/cos²x

1+5sinx/cosx=3sec²x

1+5tanx=3(1+tan²x)

1+5tanx=3+3tan²x

3tan²x-5tanx+2=0

3tan²x-3tanx-2tanx+2=0

3tanx(tanx-1)-2(tanx-1)=0

(3tanx-2)(tanx-1)=0

tanx=1,2/3

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