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Question
If A, B, C are the angles of ΔABC, then `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` = ______
Options
0
1
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-1
MCQ
Fill in the Blanks
Solution
If A, B, C are the angles of ΔABC, then `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` = 1
Explanation:
`tan(A/2 + B/2) = tan(pi/2 - C/2)`
⇒ `(tan A/2 + tan B/2)/(1 - tan A/2 tan B/2) = cot C/2`
⇒ `(tan A/2 + tan B/2)/(1 - tan A/2tan B/2) = 1/(tan C/2)`
⇒ `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2 = 1`
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Trigonometric Functions of Sum and Difference of Angles
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