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Question
Find the value of the following:
tan 15° tan 30° tan 45° tan 60° tan 75°
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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