Trigonometry


  1. The value of (sin² 25° + sin² 65°) is :









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    sin² 25° + sin² 65°
    = sin² 25° + sin² (90° - 25°)
    = sin² 25° + cos² 25° = 1

    Correct Option: B

    sin² 25° + sin² 65°
    = sin² 25° + sin² (90° - 25°)
    = sin² 25° + cos² 25° = 1


  1. The value of cos 1° cos 2° cos 3°....... cos 177° cos 178° cos 179° is :









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    cos 90° = 0
    ∴ cos 1°. cos 2° ... cos 179° = 0

    Correct Option: A

    cos 90° = 0
    ∴ cos 1°. cos 2° ... cos 179° = 0



  1. If sec θ = x +
    1
    (0° < θ < 90°), then sec θ + tan θ is equal to
    4x










  1. View Hint View Answer Discuss in Forum

    sec θ =
    4x² + 1
    4x

    tan θ = √sec² θ - 1
    [(4x² + 1 / 4x)²] - 1
    [(4x² + 1)² - (4x)² / (4x)²]
    (2x + 1)(2x - 1)
    =
    4x² - 1
    4x4x

    ∴ sec θ + tan θ =
    4x² + 1
    +
    4x² - 1
    4x4x

    =
    4x² + 1 + 4x² - 1
    4x

    =
    8x²
    = 2x
    4x

    Correct Option: B

    sec θ =
    4x² + 1
    4x

    tan θ = √sec² θ - 1
    [(4x² + 1 / 4x)²] - 1
    [(4x² + 1)² - (4x)² / (4x)²]
    (2x + 1)(2x - 1)
    =
    4x² - 1
    4x4x

    ∴ sec θ + tan θ =
    4x² + 1
    +
    4x² - 1
    4x4x

    =
    4x² + 1 + 4x² - 1
    4x

    =
    8x²
    = 2x
    4x


  1. If 7 sin²θ+ 3 cos²θ= 4 (0° ≤ θ ≤ 90°), then value of θ is









  1. View Hint View Answer Discuss in Forum

    7 sin²θ + 3 cos²θ = 4
    ⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
    ⇒ 7 sin²θ + 3 – 3 sin²θ = 4
    ⇒ 4 sin²θ = 4 – 3 = 1

    ⇒ sin²θ =
    1
    4

    ⇒ sinθ =
    1
    = sin
    π
    26


    ⇒ θ =
    π
    6

    Correct Option: C

    7 sin²θ + 3 cos²θ = 4
    ⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
    ⇒ 7 sin²θ + 3 – 3 sin²θ = 4
    ⇒ 4 sin²θ = 4 – 3 = 1

    ⇒ sin²θ =
    1
    4

    ⇒ sinθ =
    1
    = sin
    π
    26


    ⇒ θ =
    π
    6



  1. If 7 sin²θ+ 3 cos²θ= 4 (0° ≤ θ ≤ 90°), then value of θ is









  1. View Hint View Answer Discuss in Forum

    7 sin²θ + 3 cos²θ = 4
    ⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
    ⇒ 7 sin²θ + 3 – 3 sin²θ = 4
    ⇒ 4 sin²θ = 4 – 3 = 1

    ⇒ sin²θ =
    1
    4

    ⇒ sinθ =
    1
    = sin
    π
    26


    ⇒ θ =
    π
    6

    Correct Option: C

    7 sin²θ + 3 cos²θ = 4
    ⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
    ⇒ 7 sin²θ + 3 – 3 sin²θ = 4
    ⇒ 4 sin²θ = 4 – 3 = 1

    ⇒ sin²θ =
    1
    4

    ⇒ sinθ =
    1
    = sin
    π
    26


    ⇒ θ =
    π
    6