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Question

Find the value of tan35°tan40°tan45°tan50°tan55°

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Solution

Tan35.tan40.tan45.tan50.tan55
tan(90-55).tan40.1.tan(90-40).tan55
we know that, tan45 =1,and tan(90-X)=cotx
cot55.tan40.1.cot40.tan55
we know that,cotx=1/tanx
1/tan55.tan40.1.1/tan40.tan55
by solving it we get answer as 1

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