Question
If 4sin² θ = 3(1+ cos θ), 0° <
θ < 90°, then what is the value of (2tan θ + 4sinθ - secθ)?Solution
4 (1 - cos2 θ) = 3 + 3cos θ ⇒ 4 - 4cos2 θ = 3 + 3cos θ ⇒ 4cos2 θ + 3cos θ - 1 = 0 ⇒ 4cos2 θ + 4cos θ - cos θ - 1 = 0 ⇒ 4cos θ (cos θ + 1) - 1 (cos θ + 1) = 0 ⇒ (4cos θ - 1) (cos θ + 1) = 0 ⇒ cos θ + 1 = 0 ⇒ cos θ = - 1 [Not possible because 0° < θ < 90] ⇒ 4cos θ - 1 = 0 ⇒ cos θ = 1/4 We can get all value by using the image below, 
The height will be = √(42 - 12) = √(16 - 1) = √15 So, (2tan θ + 4sin θ - sec θ) = (2 × √15) + (4 × √15/4) - 4 = 2√15 + √15 - 4 = 3√15 - 4
What will come in place of (?) question mark in the given number series.
960, 960, 480, ?, 40, 8
135, 148, ?, 184, 207, 236
100, 120, 260, ?, 3220, 16120
945, 1890, ?, 504, 144, 32
84, 105, ?, 168, 210, 259
What will come in place of the question mark (?) in the following series?
17, 138, 307, 532, ?, 1182
What will come in place of the question mark (?) in the following series?
?, 65, 37, 73, 29, 81
114, 156, ?, 238, 274, 304
What will come in place of the question mark (?) in the following series?
4000, ?, 320, 192, 153.6, 153.6
24, 8, 15, ?, 12, 4
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