Question

8. Calculaţi: a) (sin 60° + tg 30°) . ctg 30°; c) (sin 45° + cos 45º)2 · cos 60°; d) b) (ctg 30° + tg 60°): sin 60°; d) (ctg 60° - cos 30°3 : sin 60° : Va rog mult URGENT​

Answer 1

Explicație pas cu pas:

a)

$(sin 60°+tg 30°) \times ctg 30° = ( \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{3} ) \times \sqrt{3} = \frac{3}{6} \times \sqrt{3} = \frac{ \sqrt{3} }{2}$

b)

$(ctg 30° + tg 60°) \div sin 60° = (\sqrt{3} + \sqrt{3} ) \div \frac{ \sqrt{3} }{2} = 2 \sqrt{3} \times \frac{2}{ \sqrt{3} } = 4$

c)

$(sin 45° + cos 45º)2 \times cos 60° = ( \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} )\times2 \times \frac{1}{2} = \frac{2 \sqrt{2} }{2} = \sqrt{2}$

d)

$(ctg 60° - cos 30°)3 \div sin 60° = ( \frac{ \sqrt{3} }{3} - \frac{ \sqrt{3} }{2} )\times3 \div \frac{ \sqrt{3} }{2} = \frac{2 \sqrt{3} - 3 \sqrt{3} }{6} \times 3 \times \frac{2}{ \sqrt{3} } = \frac{ - \sqrt{3} }{6} \times \frac{3\times2}{ \sqrt{3} } = - 1$