Question

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

Answer 1

✶⊶⊷⊶⊷❍ ❥ ❍⊶⊷⊶⊷✶

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

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

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

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

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

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

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

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

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

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

$⟹\sf\bold{\blue{\frac{2}{sinθ}}}$

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

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

✶⊶⊷⊶⊷❍ ❥ ❍⊶⊷⊶⊷✶

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

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Answer 2

this photo is your answer