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Napier’s Analogy

If sectheta p...

Question

If sectheta plus tantheta equals 4 what would be Costheta

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Solution

SecØ +TanØ=4
SecØ= 4-TanØ
squaring both sides
Sec²Ø= 16 + Tan²Ø- 8 TanØ
1+Tan²Ø=16 + Tan²Ø- 8 TanØ
we get 8Tan Ø= 15
TanØ=15/8
Tan²Ø= 225/64
Sec²Ø= 1+Tan²Ø
Sec²Ø= 289/64
SecØ =17/8
So CosØ=8/17
Sin²Ø=1-Cos²Ø = 1-64/289
Sin²Ø= 225/289
SinØ= 15/17

Then we can simply find

Cos Ø= 8/17

(By drawing triangle we know that the Pythagorean triplet are 8,15,17)

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