Question

if tana+secA=3/2 find tanA

Answer 1

Hey friend!
Here is your answer
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=> TanA+SecA= 3/2 ————-(1)

=> (SinA/CosA)+(1/CosA)= 3/2,

=> (SinA+1)/CosA= 3/2,

Now, multiplying (SinA-1) in both numerator and denominator,

=> [(Sin^2)A-1]/cosA(SinA-1)= 3/2

=> (Cos^2)A/CosA(SinA-1)= 3/2

=> CosA/(SinA-1)= 3/2,

=> 1/(TanA-SecA)= 3/2

=> TanA-SecA= 2/3————-(2)
Now plus the equation 1 & 2

TanA+secA-2/3+ TanA - secA-3/2 =0

Then cancelled secA
2tanA= 13/6
TanA = 13/12
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Hope it's helpful