The value of A-tan180-A-tan90-A-tan360-A is

nbsp;A+tan(180°+A)+tan(90°+A)+tan(360° A) = A+tan A A tan A =0 ...

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Standard XII

Mathematics

Allied Angles

The value of ...

Question

The value of $cot A + tan (180 ° + A) + tan (90 ° + A) + tan (360 ° - A)$ is

0.0

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Solution

$cot A + tan (180 ° + A) + tan (90 ° + A) + tan (360 ° - A)$
$= cot A + tan A - cot A - tan A = 0$

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Similar questions

Q. The value of

cot A + tan (180 ° + A) + tan (90 ° + A) + tan (360 ° - A)

Q. The value of

cot A + tan (180 ° + A) + tan (90 ° + A) + tan (360 ° - A)

Q. Prove that

cot A + tan (180^{\circ} + A) + tan (90^{\circ} + A) + tan (360^{\circ} - A) = 0

Prove that:

$(i) \frac{c o s (2 π + θ) c o s e c (2 π + θ) t a n (π / 2 + θ)}{s e c (π / 2 + θ) c o s θ c o t (π + θ)} = 1$

$(i i) \frac{c o s e c (90^{\circ} + θ) + c o t (450^{\circ} + θ)}{c o s e c (90^{\circ} - θ) + t a n (180^{\circ} - θ)} + \frac{t a n (180^{\circ} + θ) + s e c (180^{\circ} - θ)}{t a n (360^{\circ} + θ) - s e c (- θ)} = 2$

$(i i i) \frac{s i n (180^{\circ} + θ) c o s (90^{\circ} + θ) t a n (270^{\circ} - θ) c o t (360^{\circ} - θ)}{s i n (360^{\circ} - θ) c o s (360^{\circ} + θ) c o s e c (- θ) s i n (270^{\circ} + θ)} (i v) 1 + c o t θ - s e c (\frac{π}{2} + θ)} 1 + c o t θ + s e c (\frac{π}{2} + θ)} = 2 c o t θ$

$(v) \frac{t a n (90^{\circ} - θ) s e c (180^{\circ} - θ) s i n (- θ)}{s i n (180^{\circ} + θ) c o t (360^{\circ} - θ) c o s e c (90^{\circ} - θ)} = 1$