Math, asked by trigo2, 1 year ago

If 1+sin^2 theta = 3sin theta cos theta, then prove that tan theta =1or 1/2 

Answers

Answered by debnathayushi
1
1 + sin^2 Ø = 3sinØcosØ 
divide by cosØ 
1/cosØ + tanØsinØ = 3sinØ 
secØ + tanØsinØ = 3sinØ 
tanØ = (3sinØ - secØ)/sinØ 
= 3 - secØ/sinØ 
let's stop here: 
tanØ = 3 - 1/(sinØcosØ) ****** 

if tanØ = 1 , sinØ/cosØ = 1 and sinØ = cosØ, Ø = π/2 
in ***** 
LS = tanØ = 1 
RS = 3 - 1/sin^2 Ø 
= 3 - 1/(1/2) = 3-2 = 1 
= LS 

if tanØ = 1/2 
sinØ = 1/√5 and cosØ = 2/√5 

in ***** 
LS = 1/2 
RS = 3 - 1/(sinØcosØ) 
= 3 - 1/((1/√5)(2/√5)) 
= 3 - 1/(2/5) 
= 3 - 5/2 
= 1/2 
= LS 
[Note:-
Ø represents theta]
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