Prove that tan 20° tan 35° tan 45° tan 55° tan 70° = 1

Asked by Sakshi | 9 months ago |  120

1 Answer

Solution :-

Taking 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 × 1 × 1 = 1

Hence proved

Answered by Sakshi | 9 months ago

Related Questions

Evalute the following:

(i) \( \dfrac{sin 20°}{ cos 70°}\)

(ii) \(\dfrac{ cos 19°}{ sin 71°}\)

(iii) \( \dfrac{sin 21°}{ cos 69°}\)

(iv) \( \dfrac{tan 10°}{ cot 80°}\)

(v) \( \dfrac{sec 11°}{ cosec 79°}\)

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