Question

Sin3x/cosx + cos3x/sinx = 2cot2x prove the above

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$\red { \frac{sin 3x}{cos x} + \frac{cos 3x}{sin x }}\green {= 2 cot 2x}$

Step-by-step explanation:

$LHS = \frac{sin 3x}{cos x} + \frac{cos 3x}{sin x }\\= \frac{ sin 3x sin x + cos 3x cos x }{cos x sin x } \\= \frac{ cos 3x cos x + sin 3x sin x }{ sin x cos x }\\= \frac{ cos (3x - x)}{sin x cos x }$

$\boxed { \pink { cos A cos B + sin A sin B = cos (A - B ) }}$

$= \frac{ cos 2x}{sin x cos x }\\= \frac{2 cos 2x}{2 sin x cos x }\\= \frac{ 2cos 2x}{sin 2x }$

$\boxed { \orange { 2sin x cos x = sin 2x }}$

$= 2 cot 2x \\= RHS$

Therefore.,

$\red { \frac{sin 3x}{cos x} + \frac{cos 3x}{sin x }} \green {= 2 cot 2x}$

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