Question

a cot theta+ b cosec theta =P
b cot theta + a cosec theta
= Q
then find p² - Q²​

Answer 1

GIVEN :-

a cot theta+ b cosec theta =P

a cot theta+ b cosec theta =Pb cot theta + a cosec theta = Q

TO FIND:- P² - Q²

SOLUTION:-

GIVEN AS, A COT THETA + B COSEC THETA = P

B COT THETA + A COSEC THETA = Q

NOW P² =(A COT THETA + B COSEC THETA)²

P² = A²COT²THETA + B²COSEC²THETA ...............1

Q² = B²COT²THETA + A²COSEC²THETA................2

SO P² - Q² = (A²COT²THETA + B²COSEC²THETA + 2ABCOT THETA COSEC THETA) - (B²COT²THETA + A²COSEC²THETA 2ABCOT THETA COSEC THETA)

P² - Q² = COT²THETA ( A² - B² ) - COSEC²THETA( A² - B² )

P² - Q² = ( A² - B² ) [ COT²THETA - COSEC²THETA]

SO , P² - Q² = ( A² - B² )

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