X = If tan 9° = - then, the value of sec281 /1 + cot2 81 is :
Answers
Given : tan 9° = x/y
To Find : Sec²81° /(1 + cot²81°)
Solution:
Sec²81° /(1 + cot²81°)
cotx = cosx/sinx
= Sec²81° /(1 + cos²81°/sin²81°)
= sin²81°Sec²81°/( sin²81° + cos²81°)
sin²x + cos²x = 1
= sin²81°Sec²81°
secx = 1/cosx
= sin²81°/cos²81°
sinx/cosx = tanx
= tan²81°
tan (90° - x) = cotx
= cot²9°
cotx = 1/tanx
= 1/tan²9°
= 1/(x/y)²
= y²/x²
Sec²81° /(1 + cot²81°) = y²/x²
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Answer:
Sec²81° /(1+ cot2²81°)
cotx = cosx/sinx
= Sec²81° /(1 + cos²81%/sin²81°)
= sin²81°Sec²81/( sin²81° + cos²81°)
=
sin^2 x + cos^2 x = 1
= sin²81°Sec²81°
secx = 1/cosx
= sin²81%/cos²81°
sinx/cosx = tanx
= tan²81°
tan (90° - x) = cotx
= cot²9°
cotx = 1/tanx
= 1/tan²9°
= 1/(x/y)²
= y²/x²
Sec²81° /(1+ cot²81°) = y²/x².