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    Question

    Calculate the value of

    sec75o
    A √2(√3 – 1) Correct Answer Incorrect Answer
    B √2(√3 – 1) Correct Answer Incorrect Answer
    C √3(√2 + 1) Correct Answer Incorrect Answer
    D √3(√2 – 1) Correct Answer Incorrect Answer

    Solution

    sec75o = 1/cos75o = {1/(cos (30 + 45)o} We know that cos(a + b) = (cosacosb – sinasinb) So, cos75o = cos30o × cos45o – sin30o × sin45o So, cos75o = {(√3/2) × (1/√2) – (1/2) × (1/√2)} So, cos75o = {(√3 – 1)/2√2} So, sec75o = {2√2/(√3 – 1)} = {2√2 × (√3 + 1)}/{(√3 – 1)( (√3 + 1)} = √2(√3 + 1)

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