Math, asked by pbodada, 9 months ago

show that (cosecA-cotA
)2=1-cosA/1+cosA

Answers

Answered by Anonymous
7

Solution :-

 \tt (cosecA - cotA)^{2}  =  \dfrac{1 - cosA}{1 + cosA}

Consider RHs

 \tt  = (cosecA - cotA)^{2}

Writing cosecA and cotA in terms of cosA and sinA

 \tt  =  \bigg( \dfrac{1}{sinA}  -  \dfrac{cosA}{sinA}  \bigg)^{2}

 \tt  =  \bigg(  \dfrac{1  - cosA}{sinA}  \bigg)^{2}

 \tt  =    \dfrac{(1  - cosA) ^{2} }{sin^{2} A}

 \tt  =    \dfrac{(1  - cosA) ^{2} }{1 - cos^{2} A}

[ Because sin²A = 1 - cos²A ]

It can be written as

 \tt  =    \dfrac{(1  - cosA) ^{2} }{ 1^{2}   - cos^{2} A}

 \tt  =    \dfrac{(1  - cosA)^{2}  }{(1    + cos A)(1 - cosA)}

[ Because x² - y² = (x + y)(x - y) ]

 \tt  =    \dfrac{1  - cosA }{1    + cos A}

= RHS

LHS = RHS

Hence proved.

Answered by StarGazer001
3

Answer:

Refer to the attachment.

Attachments:
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