Simplify: 3(sin 36/cos 54)2 - 2(tan 18/cot 72)3 + 2 tan 13× tan 21×tan69×tan 77
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3(sin36°/cos54°)²-2(tan18°/cot72°)³+2tan13°tan21°tan69°tan77°
=3{sin36°/cos(90°-36°)}²-2{tan18°/cot(90°-18°)}³+2tan13°tan21°tan(90°-21°)tan(90°-13°)
=3(sin36°/sin36°)²-2(tan18°/tan18°)³+2tan13°tan21°cot21°cot13°
[∵, cos(90°-Ф)=sinФ, cot(90°-Ф)=tanФ, tan(90°-Ф)=cotФ]
=3-2+2tan13°tan21°(1/tan21°)(1/tan13°)
=1+2×1×1
=1+2
=3
=3{sin36°/cos(90°-36°)}²-2{tan18°/cot(90°-18°)}³+2tan13°tan21°tan(90°-21°)tan(90°-13°)
=3(sin36°/sin36°)²-2(tan18°/tan18°)³+2tan13°tan21°cot21°cot13°
[∵, cos(90°-Ф)=sinФ, cot(90°-Ф)=tanФ, tan(90°-Ф)=cotФ]
=3-2+2tan13°tan21°(1/tan21°)(1/tan13°)
=1+2×1×1
=1+2
=3
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