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Evaluate the following :- \sin ^{2} 25^{\circ}+\sin ^{2} 65^{\circ}+\sqrt{3}\left(\tan 5^{\circ} \tan 15^{\circ} \tan 30^{\circ} \tan 75^{\circ} \tan 85^{\circ}\right) |
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Answer» Sin²25°+sin²65°+√3(tan5°tan15°tan30°tan75°tan85°)=sin²25°+sin²(90°-25°)+√3{tan5°tan15°×(1/√3)×tan(90°-15°)tan(90°-5°)}=sin²25°+cos²25°+√3×1/√3(tan5°tan15°cot15°cot5°)=1+1=2 Ans. |
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