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)
7, 14, 42, 210, 1470, ?
A sequence {Vₙ} is defined for n ≥ 1 by:
I) For every n ≥ 3: Vₙ = 2Vₙ₋₁ − Vₙ₋₂ + 4
It is known that - V₃ = 22 and ...
12, 20, 36, ?, 132, 260
If 6 4 x 5.75 9,
Then, (x²-1) = ?
...12 13 30 �...
112 162 199 ? 242 252
...21 11.5 13 ? 45.5 116.75
...171, 173, 183, 213 , ‘?’, 411, 633.
114 106 102 100 99 ?
...Choose the correct alternative
21: 3 ∷ 574: ?
