Question

prove that sin a/(1-cos a)=cosec a+cot a
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Answer 1

Answer:

Q→ Evaluate the following limit.

$lim \: x→0 \binom{\sqrt[3]{1 + \times - \sqrt{1 + \times } } }{ \times }$

Step-by-step explanation:

Q→ Evaluate the following limit.

$lim \: x→0 \binom{\sqrt[3]{1 + \times - \sqrt{1 + \times } } }{ \times }$

Answer 2

Answer:

Taking LHS

• sina/(1-cos a)= sin a / (1-cos a) × ( 1+ cos a)/ ( 1+cos a) [ by rationalizing the denominator ( 1- cos a]
• = sina+ (sina × cos a) / ( 1)^2- (cos a)^2 [ by (a+b) (a-b)=a^2 - b^2]
• sin a + ( sina × cosa) / 1 - cos ^2 a
• sina + ( sina× cosa) / sin^2a [ sin^2a = 1 - cos ^2 a]
• sina / sin ^2a + sina cos a/ sin^2a
• 1/sin a + cos a / sin a
• cosec a + cot a [ 1/ sin a = cosec a & cos a/ sin a= cot a
• Hence LHS = RHS

PROVED

Hope it will help you.