If 2tan A- A-tan B- then the value of A-2tanA-B is

A+2tan(A B) = A+2[tan A tan B1+tan Atan B] = A+2[tan A 2tan A A1+tan A(2tan A+ A)] = A 2(tan A+ A)2(1+tan^2A) = A (tan A+1tan A)(1+tan^2A) = A A=0 ...

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Standard XIII

Mathematics

Trigonometric Ratios of Compound Angles

If 2tan A+ A=...

Question

If $2 tan A + cot A = tan B$ , then the value of $cot A + 2 tan (A - B)$ is

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Solution

The correct option is A $0$
$cot A + 2 tan (A - B) = cot A + 2 [\frac{tan A - tan B}{1 + tan A tan B}] = cot A + 2 [\frac{tan A - 2 tan A - cot A}{1 + tan A (2 tan A + cot A)}] = cot A - 2 \frac{(tan A + cot A)}{2 (1 + {tan}^{2} A)} = cot A - \frac{(tan A + \frac{1}{tan A})}{(1 + {tan}^{2} A)} = cot A - cot A = 0$

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Trigonometric Ratios of Compound Angles

Standard XIII Mathematics

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If 2tanA+cotA=tanB, then the value of cotA+2tan(A−B) is

The correct option is A 0cotA+2tan(A−B)=cotA+2[tanA−tanB1+tanAtanB]=cotA+2[tanA−2tanA−cotA1+tanA(2tanA+cotA)]=cotA−2(tanA+cotA)2(1+tan2A)=cotA−(tanA+1tanA)(1+tan2A)=cotA−cotA=0

If $2 tan A + cot A = tan B$ , then the value of $cot A + 2 tan (A - B)$ is