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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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