If tan Theta cot Theta 16 then find the ratio of tan2 Theta cot2 Theta to tan2 Theta cot2 Theta 20 t...........

Quantitative Aptitude ( CCS) Trignometry

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If tanΘ + cotΘ = 16, then find the ratio of tan²Θ + cot²Θ to tan²Θ + cot²Θ + 20 tanΘ.cotΘ

64 : 65

129 : 137

27 : 29

127 : 137

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Explanation:

Given, tanΘ + cotΘ = 16
Squaring both sides, we get
tan²Θ + 2tanΘ . cotΘ + cot²Θ = 256
or, tan²Θ + cot²Θ = 256 – 2
∴ tan²Θ + cot²Θ = 254
Now, tan²Θ + cot²Θ + 20tanΘ.cotΘ
= ( tan²Θ + cot²Θ) + 20tanΘ . 1/tanΘ
= 254 + 20 = 274
∴ Reqd. ratio = 254 /274 = 127 /137
= 127 : 137