Question

$\\\red{please \: solve \: this} \\ \pink{ = > find \: the \: value \: of \tan( \frac{\pi}{8} ) } \\ (trignometry \: class \: 11)$

Answer 1

Hey

Here is your answer,

Tan (π/8) = Tan 45°

Tan 45° = 1

Hope it helps you!

Answer 2

Hey !!!

We know that ,

tanπ / 8 = tan22 ½

tan22½° = sin22½° /cos22½ °

squaring on both sides .

tan² 22½ = 2sin²22½ / 2 cos²22½

Or , we know that ,

cos2¢ = 1 - 2sin²¢
1 - cos2¢ = 2sin²¢ -----1)

and, also , cos2¢ = 2cos²¢ - 1
cos2¢ + 1 = 2cos²¢ ----2)

From 1st and 2nd equation .

tan²22½ = 1 - cos45° / 1 + cos45°

tan²22½ = √2 - 1 / √2 + 1

rationalise it .

√2 - 1 / √2 + 1 × √2 - 1 /√2 - 1 = ( √2 - 1)² / 1

tan²22 ½ = √2 - 1 ..

since , value of tanπ/10 = √2 - 1


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$\huge \pink{mr \: perfect \: }$