giúp tớ với ạaa. Tớ cảm ơnnnn

Đáp án + Giải thích các bước giải:

a) $A = \tan \alpha - \cot \alpha$

$\Leftrightarrow A^2 = (\tan \alpha - \cot \alpha)^2$

$\Leftrightarrow A^2 = \tan^2 \alpha + \cot^2 \alpha - 2\tan \alpha \cot \alpha$

$\Leftrightarrow A^2 = (\tan \alpha + \cot \alpha)^2 - 4 \tan \alpha \cot \alpha$
$\Leftrightarrow A^2 = 49 - 4$

$\Leftrightarrow A^2 = 45$

$\Leftrightarrow A = \pm 3\sqrt{5}$

b) $B = \tan^2 \alpha - \cot^2 \alpha$

$\Leftrightarrow B = (\tan \alpha + \cot \alpha)(\tan \alpha - \cot \alpha)$

$\Leftrightarrow B = 7 . \pm 3\sqrt{5}$
$\Leftrightarrow B = \pm 21\sqrt{5}$

c) $C = \tan^2 \alpha + \cot^2 \alpha$

$\Leftrightarrow C = (\tan \alpha + \cot \alpha)^2 - 2$

$\Leftrightarrow C = 7^2 - 2$

$\Leftrightarrow C = 47$

d) $D = \tan^3 \alpha + \cot^3 \alpha$

$\Leftrightarrow D = (\tan \alpha + \cot \alpha)^3 - 3 \tan \alpha \cot \alpha (\tan \alpha + \cot \alpha)$
$\Leftrightarrow D = 7^3 - 3 . 7$

$\Leftrightarrow D = 322$

e) $E = \tan^4 \alpha + \cot^4 \alpha$

$\Leftrightarrow E = (\tan^2 \alpha + \cot^2 \alpha)^2 - 2\tan^2 \alpha \cot^2 \alpha$

$\Leftrightarrow E = 47^2 - 2 . 1$

$\Leftrightarrow E = 2207$

f) $F = \tan^5 \alpha + \cot^5 \alpha$

$\Leftrightarrow F = \tan^5 \alpha + \cot^5 \alpha + \tan^2 \alpha \cot^3 \alpha + \tan^3 \alpha\cot^2 \alpha - \tan^2 \alpha \cot^3 \alpha - \tan^3 \alpha \cot^2 \alpha$

$\Leftrightarrow F = (\tan^3 \alpha + \cot^3 \alpha)(\tan^2 \alpha + \cot^2 \alpha) - \tan^2 \alpha \cot^2 \alpha (\tan \alpha + \cot \alpha)$

$\Leftrightarrow F = 322 . 47 - 7$

$\Leftrightarrow F = 15127$