Question

if sin theta + cot theta = √3.....then prove that tan theta + cot theta = 1......​

Answer 1

Answer:

sinФ + cos Ф= √3..............eq 1

to prove tan Ф + cot Ф = 1

equation 1 squaring on both sides we get

(sinФ + cos Ф)² = √3²

using (a+ b)² identity

sin²Ф + cos ²Ф + 2 sinФ cosФ = 3

1 + 2sin Ф cos Ф = 3

2 sinФ cosФ= 3-1

2sinФcosФ=2

sinФcosФ=1 ................eq 2

to proof  

tanФ+ cotФ= 1

⇒ sinФ/cosФ + cosФ/sin Ф

taking lcm

sin²Ф + cos²Ф/cosФsinФ

from eq 2 we know sinФ cosФ = 1

⇒sin²Ф +cos²Ф/1  ( we know sin^2 Ф+ cos ^2 Ф = 1)

so we get ,

⇒1/1 = 1

hence proved

hope it helps!!!!!!!!!!!

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Answer 2

Hey

Its simple

Sin Θ + cos Θ =√3

Sin Θ = √3 - cos Θ

tan Θ = √3 - cos Θ/cos Θ

Cot Θ = cos Θ /√3 - cos Θ

tan Θ / cot Θ = 1

Hence proved

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