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Question
The value of tan 75° - cot 75° is equal to ______.
Options
`2sqrt(3)`
`2 + sqrt(3)`
`2 - sqrt(3)`
1
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Solution
The value of tan 75° – cot 75° is equal to `bbunderline(2sqrt(3))`.
Explanation:
The given expression is tan 75° − cot 75°
= `sin75^circ/cos75^circ - cos75^circ/sin75^circ`
= `(sin^2 75^circ - cos^2 75^circ)/cos75^circ sin75^circ`
= `(2sin^2 75^circ - cos^2 75^circ)/(2 cos75^circ sin75^circ)`
= `(-2cos150^circ)/(sin150^circ)`
= `-2cot150^circ`
= `- 2 cot (180^circ - 30^circ)`
= `2cot30^circ`
= `2sqrt3`
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