Question

11. Sabiendo que: tano = sen20° .csc20° + 1
4tan13° . cot13° +1
, donde o es agudo, calcule:
C = cos 0 - sen²0​

Answer 1

RESOLUCIÓN:

$tanΘ = \frac{sen20 \times csc20 + 1}{4tan13 \times cot13 + 1} \\ tanΘ = \frac{1 + 1}{4 \times 1 + 1} \\ tanΘ = \frac{2}{5}$

$C = cos {}^{2} Θ - sen {}^{2} Θ \\ C = ( \frac{5}{ \sqrt{29} } ) {}^{2} - ( \frac{2}{ \sqrt{29} } ) {}^{2} \\ C = \frac{25}{29} - \frac{4}{29} \\ C = \frac{21}{29}$