Question

show that: tan57+cot37/tan33+cot53 = tan57 cot37

Answer 1

hope this will be useful to u

Answer 2

Answer:

$\frac{tan57+cot37}{tan33+cot53}=tan57cot37$

Step-by-step explanation:

$LHS = \frac{tan57+cot37}{tan33+cot53}\\=\frac{tan57+cot37}{tan(90-57)+cot(90-37)}\\=\frac{tan57+cot37}{cot57+tan37}\\=\frac{tan57+cot37}{\frac{1}{tan57}+\frac{1}{cot37}}\\=\frac{tan57+cot37}{\frac{cot37+tan57}{tan57cot37}}\\=(tan57+cot37)\times \frac{tan57cot37}{tan57+cot37}\\=tan57cot37\\=RHS$

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