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Evaluate COS58+sn22evaluatecos58 sin22cos38 cosec52°sin32 cos68 tan18 tan35 tan60 tan72 tan55OR |
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Answer» cos 58° = cos(90 - 32°) = sin 32°sin 22° = sin(90 - 68°) = cos 68° cos 38° = cos(90 - 52°) = sin 52°tan 18° = cot 72°tan 35° = cot 55°[cos 58°/sin 32°] + [sin 22°/cos 68°] - [(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)] = [sin 32°/sin 32°] + [cos 68°/cos 68°] - [(sin 52°/sin 52°)/(cot 72° cot 55° tan 60° tan 72° tan 55°)] = [1] + [1] - [1/√3] (∵ tan 60° = √3) = (2√3 - 1)/√3 = (6 - √3)/3 (∵ Rationalise the denominator) |
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