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12 February, 07:38

1. cot x sec4x = cot x + 2 tan x + tan3x

2. (sin x) (tan x cos x - cot x cos x) = 1 - 2 cos2x

3. 1 + sec2x sin2x = sec2x

4. - tan2x + sec2x = 1

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Answers (1)
  1. 12 February, 08:18
    0
    1. cot (x) sec⁴ (x) = cot (x) + 2tan (x) + tan (3x)

    cot (x) sec⁴ (x) cot (x) sec⁴ (x)

    0 = cos⁴ (x) + 2cos⁴ (x) tan² (x) - cos⁴ (x) tan⁴ (x)

    0 = cos⁴ (x) [1] + cos⁴ (x) [2tan² (x) ] + cos⁴ (x) [tan⁴ (x) ]

    0 = cos⁴ (x) [1 + 2tan² (x) + tan⁴ (x) ]

    0 = cos⁴ (x) [1 + tan² (x) + tan² (x) + tan⁴ (4) ]

    0 = cos⁴ (x) [1 (1) + 1 (tan² (x)) + tan² (x) (1) + tan² (x) (tan² (x) ]

    0 = cos⁴ (x) [1 (1 + tan² (x)) + tan² (x) (1 + tan² (x)) ]

    0 = cos⁴ (x) (1 + tan² (x)) (1 + tan² (x))

    0 = cos⁴ (x) (1 + tan² (x)) ²

    0 = cos⁴ (x) or 0 = (1 + tan² (x)) ²

    ⁴√0 = ⁴√cos⁴ (x) or √0 = (√1 + tan² (x)) ²

    0 = cos (x) or 0 = 1 + tan² (x)

    cos⁻¹ (0) = cos⁻¹ (cos (x)) or - 1 = tan² (x)

    90 = x or √-1 = √tan² (x)

    i = tan (x)

    (No Solution)

    2. sin (x) [tan (x) cos (x) - cot (x) cos (x) ] = 1 - 2cos² (x)

    sin (x) [sin (x) - cos (x) cot (x) ] = 1 - cos² (x) - cos² (x)

    sin (x) [sin (x) ] - sin (x) [cos (x) cot (x) ] = sin² (x) - cos² (x)

    sin² (x) - cos² (x) = sin² (x) - cos² (x)

    + cos² (x) + cos² (x)

    sin² (x) = sin² (x)

    - sin² (x) - sin² (x)

    0 = 0

    3. 1 + sec² (x) sin² (x) = sec² (x)

    sec² (x) sec² (x)

    cos² (x) + sin² (x) = 1

    cos² (x) = 1 - sin² (x)

    √cos² (x) = √ (1 - sin² (x))

    cos (x) = √ (1 - sin² (x))

    cos⁻¹ (cos (x)) = cos⁻¹ (√1 - sin² (x))

    x = 0

    4. - tan² (x) + sec² (x) = 1

    -1 - 1

    tan² (x) - sec² (x) = - 1

    tan² (x) = - 1 + sec²

    √tan² (x) = √ (-1 + sec² (x))

    tan (x) = √ (-1 + sec² (x))

    tan⁻¹ (tan (x)) = tan⁻¹ (√ (-1 + sec² (x))

    x = 0
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