Trigonometry Questions and Answers

  • Q1:

    The value of \(\frac{\text{sin } 45^\circ + \text{ sin } 105^\circ + \text{ cos } 105^\circ \text{ cos } 45^\circ} { \text{sin } 75^\circ + \text{ cos } 75^\circ } \) is euqal to

    1. (A)\(\frac{1}{\sqrt6}\)
    2. (B)\(\frac{1}{\sqrt3}\)
    3. (C)\(\frac{1}{2\sqrt3}\)
    4. (D)\(\frac{1}{3\sqrt2}\)
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  • Q2:

    If \(\text{ tan}x + \text{cot}x = 3, \text{then sec}^2x + \text{cosec}^2x \) is equal to 

    1. (A)3
    2. (B)9
    3. (C)12
    4. (D)15
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  • Q3:

    Two boys are on opposite sides of a tower of 100 meter height. If they measure the elevation of the top of the tower as \(30^\circ\) and \(45^\circ\) respectively, the distance between the tower is 200 metres, then the distance between the boys is

    1. (A)\(100\sqrt3 \text{ metres}\)
    2. (B)\(100(\sqrt3 + 1) \text{ metres}\)
    3. (C)\(100(\sqrt3 - 1) \text{ metres}\)
    4. (D)\(100\sqrt3 + 1 \text{ metres}\)
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  • Q4:

    For \(\lambda \ne 0\), the angle between the lines given by the equation \(\lambda y^2 + (1 - \lambda^2) \; xy - \lambda x^2 = 0 \) is

    1. (A)\(30^\circ\)
    2. (B)\(45^\circ\)
    3. (C)\(60^\circ\)
    4. (D)\(90^\circ\)
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  • Q5:

    If \(\text{cos } \alpha + \text{sec } \alpha = 2 \), then the value of \(\text{cos}^8 \alpha + \text{sec}^8 \alpha \) is equal to

    1. (A)\(2\)
    2. (B)\(2^2\)
    3. (C)\(2^4\)
    4. (D)\(2^8\)
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