Question
If a cot θ + b cosec θ = p and b cot θ + a cosec θ =
q then p² - q² is equal to_________.Solution
ATQ, Given, a cotθ + b cscθ = p b cotθ + a cscθ = q ⇒p2 − q2 = (p−q)(p+q) =[a cotθ + b cscθ − b cotθ − a cscθ][a cotθ + b cscθ + b cotθ + a cscθ] =[cotθ(a−b) − cscθ(a−b)][cotθ(a+b) + cscθ(a+b)] =(a − b)(cotθ − cscθ)(a+b)(cotθ + cscθ) =(a2 − b2)(cot2θ − csc2θ) =(−1)(a2 − b2) [∵csc2θ − cot2θ=1] =(b2 − a2)
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