Question

Prove that:
1. tan35°tan40°tan45°tan50°tan55°=1

Answer 1

 at first we can write 

tan35 = tan(90-55) = cot55

tan40 = tan(90-50) = cot50

tan45 = 1

then,

1.tan35 tan40 tan45 tan50 tan55 = 1
1.tan(90-55) tan(90-50). 1.tan 50 tan55 = 1
cot55 cot50 tan50 tan55 =1
cot55 cot50 1/cot50 1/cot55 = 1
1 = 1

Answer 2

Hence proved that Tan35°Tan40°Tan45°Tan50°Tan55° = 1

Step-by-step explanation:

To prove,

Tan35°Tan40°Tan45°Tan50°tan55° = 1

so,

Tan35° * Tan40° * Tan45° *Tan50° * Tan55°

= Tan(90°- 55°) * Tan(90°-50°) * Tan45° * Tan 50° * Tan55°

= Cot55° * Cot50° * 1 * Tan50° * Tan55°

= 1/Tan55° * 1/Tan50° * Tan50° * Tan55°

by canceling Tan50° * Tan55° with Tan50° and Tan55°,

= 1

Hence proved that,

tan35°tan40°tan45°tan50°tan55° = 1

Learn more: Trigonometry

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