if a cot? + b cosec? = p and b cot? + a cosec? = q, find p2-q2

Asked by Renoy Gladson | 13th Jul, 2013, 03:24: PM

Expert Answer:

p^2-q^2
= (a cot? + b cosec?)^2 - (b cot? + a cosec?)^2
= (a^2cot^2? + b^2cosec^2? + 2abcot?cosec? )- (b^2cot^2? + a^2cosec^2? + 2abcot?cosec?)
= cot^2? (a^2-b^2) + cosec^2? (b^2-a^2) 
= (a^2-b^2) ( cot^2? - cosec^2?)
Now, 1+ cot^2? = cosec^2?
= (a^2-b^2) (-1)
= b^2-a^2

Answered by  | 13th Jul, 2013, 07:16: PM

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