Question

tan 10°×tan15°×tan75°×tan80°=1 prove that L.H.S is equal toR.H.S.

Answer 1

Tan 10 *tan15*tan75*tan80
Cot (90-10)*cot(90-15)tan75 * tan80
Cot 80*cot 75*tan75*tan80
Tan theta*cot theta=1
So 1=1
Hence proved

Answer 2

let us take LHS.

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