Question

1÷Cos C = ans tha question plz ​

Answer 1

$\Huge{\purple{\underline{\textsf{Question}}}}$

$\leadsto⇝ \sf cos 2C = \frac{cos(A + C)}{cos(A - C)}$

Then,

⇝$\Huge{\red{\underline{\textsf{Answer}}}}$

$\leadsto \sf cos 2B = \frac{cos(A + C)}{cos(A - C)}$

$\leadsto\sf \frac{cos 2B}{1} = \frac{cos(A + C)}{cos(A - C)}$

$\leadsto \sf \frac{cos 2B + 1}{cos 2B - 1} = \frac{cos(A + C) + cos(A - C)}{cos(A + C) - cos(A - C)}$

$\leadsto \sf \frac{2 sin^{2}B}{2 cos^{2}B} = \frac{2 sin A\: sin C}{2 cos A \:cos C}$

$\leadsto \sf tan^{2}B = tan A\:tan Ctan$

$\pink\leadsto\boxed{\pink{\sf \frac{tan A}{tan B} = \frac{tan B}{tan C}}}$

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