You want to use Newton's second law in the x and y direction and set each equation equal to zero since the chandelier isn't accelerating.

FORCES IN THE X:

-T1*cos(θ1) + T2*cos(θ2) = 0

If you look at the figure, you'll notice that the x components of the tensions point in opposite direction.

T1*cos(θ1) = T2*cos(θ2)

Since you want to find an expression for T1 in terms of T2, solve for T2.

==(1)==> T2 = T1*cos(θ1) / cos(θ2)

FORCES IN THE Y:

T1*sin(θ1) + T2*sin(θ2) - mg = 0

==(2)==> T1*sin(θ1) + T2*sin(θ2) = mg

Since you want to find an expression for T1 in terms of T2, substitute equation (1) into equation (2) for T2:

T1*sin(θ1) + T1*cos(θ1)*sin(θ2)/cos(θ2) = mg

But sin(θ2)/cos(θ2) = tan(θ2)

T1*sin(θ1) + T1*cos(θ1)*tan(θ2) = mg

T1[sin(θ1) + cos(θ1)*tan(θ2)] = mg

EXPRESSION FOR T1 INDEPENDENT OF T2:

==> T1 = mg / [sin(θ1) + cos(θ1)*tan(θ2)]

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