Simplifying, I have \frac{1}{\sin x\cos x}=3

dooporpplauttssg

dooporpplauttssg

Answered question

2022-04-26

Simplifying, I have
1sinxcosx=3

Answer & Explanation

attefrimibeocx

attefrimibeocx

Beginner2022-04-27Added 14 answers

We have sin(x)cos(x)=13. This gives us that
sin2(x)cos2(x)=19sin2(x)(1sin2(x))=19
Setting sin2(x)=t, we obtain a quadratic in t, i.e.,
t(1t)=19t2t+19=0(t12)2
=1419=536t=12±56
Hence, we have sin2(x)=3±56. Since we are looking for x in the first quadrant, sin(x) has to be positive. Hence, we obtain
x=arcsin(3±56)

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