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
612, 487,?, 396, 388, 387
Find the missing number in the given number series.
1, 2, 6, 24, 120, ?What will come in place of the question mark (?) in the following series?
36, 85, ?, 230, 330, 451
Find the missing term in the series:
2, 5, 11, 23, 47, ?
What will come in place of the question mark (?) in the following series?
400, 841, 1202, ?, 1716, 1885
44   45    41   50    ?      59    23
...221, 100, 0, -81, ?
...900 Â Â Â 90Â Â Â 18Â Â Â ? Â Â Â Â 2.16Â Â Â Â 1.08
16, 20, 11, 27, ?, 38
37, 57, 82, ?, 147, 187
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