One of the most important and conceptual question from trigonometry topic trigonometric identities in which we have to find the value of tan1°tan2°…….tan89° by using trigonometric formulas
Kindly give me a detailed solution of this question as it is already asked in various examinations
RS Aggarwal, Class 10, chapter 13C, question no 28
tan1∘tan2∘tan3∘...tan89∘
=tan1∘tan2∘tan3∘...tan87∘tan88∘tan89∘
=tan1∘tan2∘tan3∘...tan(90∘−3∘)tan(90∘−2∘)tan(90∘−1∘)
=tan1∘tan2∘tan3∘...cot3∘cot2∘cot1∘
=(tan1∘cot1∘)(tan2∘cot2∘)(tan2∘cot2∘)...(tan45∘cot45∘)
since tanθcotθ=1
=1×1×1×...×1
=1