Question

tan 20° tan 35° tan 45° tan 55° tan 70° =1​

Answer 1

L.H.S = tan 20° tan 35° tan 45° tan 55° tan 70°

= tan (90° − 70°) tan (90° − 55°) tan 45°tan 55° tan70°

= cot 70°cot 55° tan 45° tan 55° tan 70°

[∵ tan (90 – θ) = cot θ]

= (tan 70° cot 70°)(tan 55° cot 55°) tan 45°

[∵ tan θ x cot θ = 1]

= 1 x 1 x 1 = 1

Hence proved.......

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