Question

plzz solved kardo.. ​

Answer 1

✭$\mathsf{To \: Prove \: : \: \sqrt{ \dfrac{1 \: - \: cos \: A }{1 \: + \: cos \: A}}\: = \: cosec \: A \: - \: cot \: A}$✭

$\mathsf{LHS\:= \:\sqrt{\dfrac{1\:-\:cos\:A}{1\:+\:cos\:A}}}$

$\textsf{Rationalizing the Denominator,}$

$\mathsf{=\:\sqrt{\left(\dfrac{1\: -\:cos\:A}{1\:+\:cos\:A}\right)\:\times\:\left(\dfrac{1\:-\:cos\:A}{1\:-\:cos\:A}\right)}}}$

$\mathsf{= \: \sqrt{\dfrac{(1 \: - \: cos \: A)^{2}}{( 1^{2} \: - \: {cos}^{2}A)}}}$

$\mathsf{= \: \dfrac{1 \: - \: cos \: A}{\sqrt{1 \: - \: {cos}^{2}A}}}$

$\mathsf{=\: \dfrac{1 \: - \: cos \: A}{\sqrt{{sin}^{2}A}}}$

$\mathsf{= \: \dfrac{ 1 \: - \: cos \: A}{sin \: A}}$$\mathsf{=\: \dfrac{1}{sin \: A} \: - \: \dfrac{cos \: A}{sin \: A}}$

$\mathsf{\implies\:cosec\:A\: -\:cot\:A\\\fbox{=RHS}}</p><p>$

✰$\boxed{\underline{\mathsf{Proved !! }}}$✰

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Note:-

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Answer 2

Answer:

ToProve⤵️:

1+cosA

1−cosA

=cosecA−cotA ✭

LHS=

1+cosA

1−cosA

Step-by-step explanation:

hope it helps