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Without using trigonometric tables prove that tan 1 degree tan 11 degree tan 21 degree tan 69 degree tan 79 degree tan 89 degree=1

Answer»

tan1°tan11°tan21°tan69°tan79°tan89°


(tanθ=1/cotθ)


⇒tan1°.tan11°.tan21°.1/cot69°.1/cot79°.1/cot89°


cot(90-θ)=tanθ


⇒tan1°.tan11°.tan21°.1/tan1°.1/tan11°.1/tan21°

= 1



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