Question

Answer 1

a: \(\sin^243^0+\sin^244^0+\sin^245^0+\sin^246^0+\sin^247^0\)

\(=\left(\sin^243^0+\sin^247^0\right)+\left(\sin^244^0+\sin^246^0\right)+\sin^245^0\)

\(=\left(\sin^243^0+cos^243^0\right)+\left(\sin^244^0+cos^244^0\right)+\frac12\)

=1+1+1/2

=2,5

b: \(cos^21^0+cos^22^0+\cdots+cos^289^0\)

\(=\left(cos^21^0+cos^289^0\right)+\left(cos^22^0+cos^288^0\right)+\cdots+\left(cos^244^0+cos^246^0\right)+cos^245^0\)

=1+1+...+1+1/2

\(=44,5\)

c: \(\sqrt{4\cdot\frac{\tan22^0}{\cot68^0}}+\tan56^0\cdot\cot56^0\)

\(=\sqrt{4\cdot\frac{\tan22^0}{\cot22^0}}+1\)

\(=\sqrt4+1=2+1=3\)