Question

Prove that:
(1 + cosθ + sinθ )/(1 + cosθ - sinθ ) = (1 + sinθ )/cosθ​

Answer 1

Answer:

${\bf{\green{(1 - cosθ + sinθ )/(-1 + cosθ + sinθ )}}}$

${\bf{\red{= (1 + sinθ )/cosθ}}}$

${\bf{\blue{LHS, }}}$

${\bf{\pink{(1-cosθ+sinθ)/(-1+cosθ+sinθ)}}}$

${\bf{\green{Divide by cosθ}}}$

${\bf{\orange{(1-cosθ+sinθ)/cosθ/(1+cosθ-sinθ)/cosθ}}}$

${\bf{\blue{(secθ-1+tanθ)/(-secθ+1+tanθ)}}}$

${\bf{\red{(secθ+tanθ) - 1/(secθ-tanθ+1)}}}$

${\bf{\green{</p><p>(secθ+tanθ)-(sec^2θ-tan^2θ)/(-secθ+tanθ+1)}}}$

${\bf{\pink{(secθ+tanθ)-((secθ+tanθ)(secθ-tanθ))/(-secθ+tanθ+1)}}}$

${\bf{\blue{(secθ+tanθ)(1-(secθ-tanθ)/(-secθ+tanθ+1)}}}$

${\bf{\red{(secθ+tanθ)(1-secθ+tanθ)/(-secθ+tanθ+1)}}}$

${\bf{\blue{(secθ+tanθ)(1-secθ+tanθ)/(1-secθ+tanθ)}}}$

${\bf{\pink{(secθ+tanθ)}}}$

${\bf{\green{(1/cosθ+sinθ/cosθ)}}}$

${\bf{\orange{(1+sinθ)/cosθ RHS}}}$

${\bf{\blue{HENCE PROVED... }}}$

Answer 2

Answer:

Answer:

✶⊶⊷⊶⊷❍ ❥ ❍⊶⊷⊶⊷✶

$\large\green{\mid{\fbox{\tt{Ꭲօ թɾօѵҽ}}\mid}}$

$\frac{sinθ}{1+cosθ}+\frac{1+cosθ}{sinθ}=2cosecθ$

$\large\red{\mid{\fbox{\tt{รοℓυƭเօɳ}}\mid}}$

$\large\pink{\mid{\fbox{\tt{ᏞᎻร}}\mid}}$=

$⟹\sf\bold{\blue{\frac{sinθ}{1+cosθ}+\frac{1+cosθ}{sinθ}}}$

$⟹\sf\bold{\blue{\frac{sin²+(1+cosθ)²}{(1+cosθ)sinθ}}}$

$⟹\sf\bold{\blue{\frac{sin²+1+cos²θ+2cosθ}{(1+cosθ)sinθ}}}$

$⟹\sf\bold{\blue{\frac{sin²+cos²θ+1+2cosθ}{(1+cosθ)sinθ}}}$

$⟹\sf\bold{\blue{\frac{2+2cosθ}{(1+cosθ)sinθ}}}$

$⟹\sf\bold{\blue{\frac{2(1+cosθ)}{(1+cosθ)sinθ}}}$

$⟹\sf\bold{\blue{\frac{2}{sinθ}}}$

$⟹\large\pink{\mid{\fbox{\tt{2.coseθ}}\mid}}$

$\large\pink{\mid{\fbox{\tt{ᏞᎻร=ƦᎻร}}\mid}}$

✶⊶⊷⊶⊷❍ ❥ ❍⊶⊷⊶⊷✶

_________________________________⠀⠀⠀⠀

⠀⠀⠀ $\large\green{\mid{\fbox{\tt{❥ϐℓυєᴇყεร}}\mid}}$

_________________________________⠀