Math, asked by rishisourav5, 9 months ago

Prove This
$\frac{tanQ}{(1 - cotQ)} + \frac{cotQ}{(1 - tanQ)} = (1 + secQcosecQ)$

Answers

Answered by Anonymous

11

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$ $<body bgcolor="</strong><strong>silver</strong><strong> ">$

$<font color="</strong><strong>gold</strong><strong>">$

$\bold{\frac{tanQ}{(1 - cotQ)} + \frac{cotQ}{(1 - tanQ)} = (1 + secQcosecQ)}$

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 $<font color=lime>$

$\bold{LHS=RHS}$ $<font color=cyan>$

$\bold{Hence proved}$

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