Question

tan 1 degree,tan 2 degree, tan 3 degree .......tan 98 degree=1 .Prove that .

Answer 1

Answer:

The right question is ....tan 89. Till tan 1 to 45 leave it as it is. From tan 46 to convert to cot. tan and cot cancelled and PRESTO proved

Answer 2

Answer:

tan 1° x tan 2° x tan 3° x .....tan 45°.......x tan 88°  x tan 89°

Here,

By complementary angles

tanθ = cotθ = 1/tanθ

tan 1° = 1/tan 89°

tan 2° = 1/tan 88°

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tan 44°= 1/tan 46°

∴ tan 1° x tan 2° x tan 3° x .....tan 45°.......x tan 88°  x tan 89°  = tan 45° =1

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