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    Question

    What is the value of

    cos75°? 
    A (√2 – 1) Correct Answer Incorrect Answer
    B (√2/4) × (√3 – 1) Correct Answer Incorrect Answer
    C (√3 – 1) Correct Answer Incorrect Answer
    D (√3/6) × (√3 – 1) Correct Answer Incorrect Answer

    Solution

    cos75o = cos(45 + 30)o Since, cos(A + B) = cosAcosB – sinAsinB So, cos 75o = cos45ocos30o – sin45osin30o = {(1/√2) × (√3/2) – (1/√2) × (1/2)} = (√3/2√2) – (1/2√2) = (1/2√2) × (√3 – 1) On multiplying both numerator and denominator by √2, we have; = (√2/4) × (√3 – 1)

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