Question

cosec theta + cot theta equal to q
show that cosec theta minus cot theta equal to 1 by q​

Answer 1

Answer:

Cosec theta + cot theta = q

Cosec square theta - cot square theta =1

From here

(cosec theta + cot theta ) (cosec theta - cot theta ) = 1

q(cosec theta - cot theta ) = 1

Cosec theta - cot theta =1/q

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Answer 2

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⭐${\blue{Explanation}}$⭐

cosec theta + cot theta = q

According to identity,

cot² theta + 1 = cosec² theta

Solving equation, we get

cosec² theta - cot² theta = 1

By identity a²-b² = (a+b)(a-b), we get

(cosec theta +cot theta)(cosec theta - cot theta) = 1

cosec theta + cot theta = 1/(cosec theta - cot theta)

Putting this value of cosec theta +cot theta in given equation (cosec theta +cot theta = q), we get

1/(cosec theta - cot theta) = q

By cross multiply we get

cosec theta - cot theta = 1/q = RHS

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