Prove This

1.	Prove This
Answer» $\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$ $\text{[math]}$ $\text{[math]}$ $\bold{\frac{tanQ}{(1 - cotQ)} + \frac{cotQ}{(1 - tanQ)} = (1 + secQcosecQ)}$ LHS, $\bold{\frac{sinQ}{cosQ} /\frac{1-cosQ} {sinQ} +\frac{cosQ}{sinQ} /\frac{1-sinQ} {cosQ}}$ $\bold{\frac{SinQ}{cosQ} /\frac{sinQ-cosQ} {sinQ} +\frac{cosQ}{sinQ} /\frac{cosQ-sinQ}{cosQ}}$ $\bold{\frac{sin^2Q}{cosQ(sinQ-cosQ)} +\frac{cos^2Q}{sinQ(cosQ-sinQ)}}$ $\bold{\frac{sin^3Q+cos^3Q} {sinQcosQ(sinQ-cosQ)}}$ $\bold{\frac{(sinQ-cosQ)(sin^2Q+cos^2Q+sinQcosQ)}{sinQcosQ(sinQ-cosQ)}}$ $\bold{\frac{sin^2Q+cos^2Q+sinQcosQ} {sinQcosQ}}$ $\bold{\frac{1+sinQcosQ}{sinQcosQ}}$ $\bold{\frac{1}{sinQcosQ}+1}$ $\bold{cosecQsecQ+1}$ . RHS $\text{[math]}$ $\bold{LHS=RHS}$ $\text{[math]}$ $\bold{Hence proved}$

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