Question

if a cotx + b cosecx = p and b cotx + a cosecx = q then p^2 - q^2 is rqual to​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

b^2 - a^2

Step-by-step explanation:

Given, a cotx + b cosecx = p

b cotx + a cosecx = q

p^2 = a^2 (cotx)^2 + b^2 (cosecx)^2 + ab (cotx)(cosecx)

q^2 = b^2 (cotx)^2 + a^2 (cosecx)^2 + ab (cotx)(cosecx)

then,

p^2 - q^2 = a^2 (cotx)^2 + b^2 (cosecx)^2 + ab (cotx)(cosecx) - [b^2 (cotx)^2 + a^2 (cosecx)^2 + ab (cotx)(cosecx)]

= a^2 (cotx)^2 + b^2 (cosecx)^2 + ab (cotx)(cosecx) - b^2 (cotx)^2 - a^2 (cosecx)^2 - ab (cotx)(cosecx)

= (a^2 - b^2) (cotx)^2 + (b^2 - a^2) (cosecx)^2

= (a^2 - b^2) (cotx)^2 - (a^2 - b^2) (cosecx)^2

= (a^2 - b^2) {(cotx)^2 - (cosecx)^2}

= (a^2 - b^2) {(-1)}

= b^2 - a^2