Question

Prove that tan80=tan10 +2tan70

Answer 1

tan 80 = (tan 10 + tan 70) / 1-tan10tan70 tan80 - tan10tan70tan80 = tan10 + tan70 tan80 - tan70 = tan10 + tan70 tan80 = tan10 + 2tan70 hence proved

Answer 2

Answer:

$tan80=tan10+2tan70$

Step-by-step explanation:

$LHS=tan80\\=tan(10+70)\\=\frac{tan10+tan70)}{1-tan10tan70}$

$We\:know\:that\\\boxed {tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}}$

$\implies tan80(1-tan10tan70)\\=tan10+tan70$

$\implies tan80-tan10tan70tan80\\=tan10+tan70$

$\implies tan80\\=tan10+tan70+tan10tan70tan80$

$\implies tan80\\=tan10+tan70+tan10tan70tan(90-10)\\=tan10+tan70+tan10tan70cot10\\=tan10+tan70+(tan10cot10)tan70\\=tan10+tan70+tan70\\=tan10+2tan70\\=RHS$

Therefore,

$tan80=tan10+2tan70$

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