If tan theta + cot theta = 5 , then find tan square theta + cot square theta
Answers
Answered by
403
Answer:
This is a very simple question of trigonometry. Let theta = ∅
Step-by-step explanation:
It is given that tan∅ + cot∅ = 5
On squaring the above equation, we get tan²∅ + cot²∅ + 2 tan∅.cot∅ = 5²
tan²∅ + cot²∅ + 2 = 25 ( tan∅.cot∅ = tan∅.(1/tan∅) = 1)
Therefore, tan²∅ + cot²∅ = 23.
Hence, the value of tan²∅ + cot ²∅ = 23
Answered by
2
Concept Introduction:
The ratio of the length of the opposite side to the length of the adjacent side is equal to the Tan theta of right angled triangle.
Given:
We have been given, tanθ+cotθ=5
To Find:
tan ^2 θ+cot^2 θ
Solution:
Given,
tanθ+cotθ=5
Now squaring both sides we get,
or, (tan^2 θ+cot^2θ+2.tanθ.cotθ)=25
or, tan^2 θ+cot^2 θ=25−2 [ Since tanθ.cotθ=1]
or, tan^2 θ+cot^2 θ=23.
Final Answer:
tan^2 θ+cot^2 θ=23
#SPJ2
Similar questions
English,
8 months ago
World Languages,
8 months ago
Science,
8 months ago
Math,
1 year ago
English,
1 year ago