Question

show that: tan10° tan15° tan75° tan80°= 1

Answer 1

<br> =tan10×tan15×tan75×tan80   =tan10×tan15×tan(90-15)×tan(90-10)  = (cot10)(cot75)(tan75)(tan10)   ={tan10(1/tan10)} {tan75(1/tan75)}   =1×1 =1 =RHS

Answer 2

L. H. S: tan (90-80)×tan (90-75)×tan75×tan80 cot80×cot75×tan75×tan80 1/tan80×1/tan75×tan75×tan80 1.    R. H. S=1   L. H.  S= R.H. S   Hence proved       Hope it helps....