As per given diagram, the sphere remains in equilibrium when, net horizontal and vertical forces are equal to zero.
i.e., ∑Fx=0⇒P−T‌sin‌θ=0 ⇒P=T‌sin‌θ ...(i) and ∑Fy=0⇒W−T‌cos‌θ=0 W=T‌cos‌θ ...(ii) By dividing Eq. (i) by Eq. (ii), we get
P
W
=
T‌sin‌θ
T‌cos‌θ
⇒P=W‌tan‌θ and their vector sum is also zero. i.e. T+P+W=0 Resultant of P and W is also equal and opposite to tension T ∴T2=P2+w2 That's why, equation T=P+W is the only incorrect expression.