Question

Write the value of tan 1degree tan 2degree... tan 89degree.

Solution with explanation also


Class 10

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Answer 1

Given : (tan 1° tan 2° tan 3° ....... tan 89°).

= > tan(90 - 89)tan(90 - 88)tan(90 - 87)....tan(90 - 46) * tan 45... tan89

We know that tan(90 - Ф) = cotФ.

= > cot89 * cot88 * cot87...... cot46 * tan 45 * ..... tan 89.

We know that cotФ = (1/tanФ)

= > (1/tan89) * (1/tan 88) * (1/tan 87) ....... (1/tan 46) tan 45 * tan 46 * ...... tan 89

= > tan 45

= > 1.

Hope it helps!