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Question
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
Options
`1/x + y`
`1/(xy)`
`1/x - 1/y`
`1/x + 1/y`
MCQ
Fill in the Blanks
Solution
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = `underlinebb(1/x + 1/y)`.
Explanation:
cot(A – B) = `1/(tan(A - B))`
= `(1 + tan A tan B)/(tan A - tan B)`
= `1/(tan A - tan B) + (tan A tan B)/(tan A - tan B)`
= `1/x + 1/y`
shaalaa.com
Trigonometric Functions of Sum and Difference of Angles
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