Question

sin a / 1 - cos a = cosec A + cot a prove that​

Answer 1

❥${\underline{\underline{\huge{\mathtt{Question:-}}}}}$

Prove that,

${\bold{\frac{sinA}{1-cosA}=cosecA+cotA}}$

❥${\underline{\underline{\huge{\mathtt{Solution:-}}}}}$

† Taking L.H.S †

${\bold{\frac{sinA}{1-cosA}}}$

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★Multiply numerator and denominator with (1+cosA)★

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${\bold{→\frac{sinA(1+cosA)}{(1-cosA)(1+cosA)}}}$

${\bold{→\frac{sinA(1+cosA)}{(1-cos^2A)}}}$

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★We know that 1-cos²A = sin²A★

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${\bold{→\frac{sinA+sinA.cosA}{sin^2A}}}$

${\bold{→\frac{sinA}{sin^2A}+\frac{sinA.cosA}{sin^2A}}}$

${\bold{→\frac{1}{sinA}+{cosA}{sinA}}}$

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★We know that 1/sinA= cosecA and cosA/sinA= cotA★

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${\red{\bold{cosecA+cotA}}}$

.•.${\boxed{\green{\bold{L.H.S=R.H.S}}}}$

Hence proved_____________!!

❥${\underline{\underline{\large{\mathtt{More\: information:-}}}}}$

Some formulas related trigonometry:-

• sin²A + cos²A = 1
• 1+tan²A = sec²A
• 1+cot²A = cosec²A

Answer 2

$\large\underline\mathrm{Solution}$

$\huge \mathfrak{L.H.S:-}$

$\implies$ sinA/(1 - cosA)

• multiple numerator and denominator with (1 + cosA)

$\implies$ sinA(1 + cosA)/(1 - cosA)(1 + cosA)

$\implies$ sinA(1 + cosA)/(1 + cos²A)

$\large\underline\mathrm{Now, \: \: [(1 \; - \; cosA²) \: = \: sin²A]}$

$\implies$ sinA + sinA.cosA / sin²A

$\implies$ sinA/sin²A + sinA.cosA/sin²A

$\implies$ 1/sinA + cosA/sinA

$\implies$ cosecA + cotA.

$\huge \mathfrak{L.H.S \: = \: R.H.S:-}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$