Question

please answer fast..... class XI trigonometry ratios of associated angles

Answer 1

heya...!!!!

we know that:-

tan(180 + ∅)= tan∅
tan(90 - ∅) = cot∅
cot∅ = 1/tan∅


NOW,

tan181°×tan182×tan183.......tan267 × tan 268 × tan269

=> tan1×tan2×........×tan87×tan88×tan89


=>tan1×tan2.....tan44×tan45×tan46×.......×tan88×tan89

=> tan1×tan2....tan44×1×tan(90 - 44)×........×tan(90 - 2)×tan(90 - 1)

=> tan1×tan3.....×tan44×cot44×......cot2×cot1

=> tan1×1/tan1×tan2×1/tan2 ......×tan44×1/tan44

=> 1×1×1×1×.........1×1×1

=> 1