sec^2 10 degree-cot^2 80 degree=
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Trigonometry identities
- cosec²x - cot²x = 1
- sec²x - tan²x = 1
The Trigonometry identities require both the angles to be same. So we will try to convert to same angle.
By the formula
sec x = cosec ( 90 - x)
sec 10 = cosec ( 90 - 10) = cosec 80.
Given question,
⇒sec²10 - cot²80
⇒ cosec²80 - cot²80
⇒ 1
By the formula
cot x = tan ( 90 - x)
cot 80 = tan ( 90 - 80) = tan 10
Given question,
⇒sec²10 - cot²80
⇒ sec²10 - tan²10
⇒ 1
Therefore, The required answer is 1, Option A.
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