Find the possible values of tan x, if cosx + 5 sin x . cos x = 3.
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Answer:
tanx=1,2/3
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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