Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th
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Find the value of the following: tan 15° tan 30° tan 45° tan 60° tan 75° - Mathematics

Sum

Find the value of the following:

tan 15° tan 30° tan 45° tan 60° tan 75°

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Solution

tan 30° = `1/sqrt(3)`, tan 45° = 1, tan 60° = `sqrt(3)`

tan 15° . tan 30°. tan 45° . tan 60°. tan 75° = `tan 15^circ * 1/sqrt(3) * 1 * sqrt(3) tan 75^circ`

= `tan 15^circ xx tan 75^circ xx 1/sqrt(3) xx 1 xx sqrt(3)`

= `tan(90^circ - 75^circ) xx 1/(cot75^circ) xx 1` ...[tan 90° – θ = cot θ]

= `cot 75^circ xx 1/(cot75^circ) xx 1`

= 1

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APPEARS IN

Samacheer Kalvi Mathematics Class 9th Tamil Nadu State Board
Chapter 6 Trigonometry
Exercise 6.3 | Q 1. (iii) | Page 235
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