Question
If sinθ + cosθ = 2a and tanθ + cotθ = b, then find a
in terms of b.Solution
Start with sinθ + cosθ = 2a. Squaring both sides gives: sin²θ + cos²θ + 2sinθcosθ = 4a². Using sin²θ + cos²θ = 1: 1 + 2sinθcosθ = 4a². Then, we know from tanθ + cotθ = b, that: tanθ + cotθ = sinθ/cosθ + cosθ/sinθ = (sin²θ + cos²θ)/sinθcosθ = 1/sinθcosθ = b. Therefore: sinθcosθ = 1/b. Substituting back, we have: 1 + 2(1/b) = 4a². Rearranging gives: 4a² = 1 + 2/b. Thus, we can solve for a in terms of b: a = √(1 + 2/b)/2. Correct answer : b) √(1 + 2/b)/2.
8, 9, 125, ?, 1331, 169Â
What value should come in the place of (?) in the following number series?
14, 18, ?, 43, 68, 104
In each of the following series, one term is missing. Find the missing term.
5, 13, 29, 61, 125, ?
96, 144, ?, 324, 486, 729, 1093.5
8, 15, 44, 175, 874, ?
12, 36, 80, 164, 328, ?
1, 6, 27, 124, ?, 3906, 27391
...251, 130, 274, ?, 301, 76Â
1056Â Â Â Â Â 264Â Â Â Â Â Â 132 Â Â Â Â Â Â 33Â Â Â Â Â Â ? Â Â Â Â Â Â 4.125
...14.8% of 7200 – 16.4% of 6200 + 15.09% of 8100 = 10% of ?
