Solution
9
a)
[tex]\begin{gathered} \cos \left(61\right)+\sin \left(29\right) \\ \\ \mathrm{Use\:the\:following\:identity}:\quad \cos \left(x\right)=\sin \left(90^{\circ \:}-x\right) \\ \\ \cos \left(61^{\circ \:}\right)=\sin \left(90^{\circ \:}-61^{\circ \:}\right) \\ \\ =\sin \left(90^{\circ \:}-61^{\circ \:}\right)+\sin \left(29^{\circ \:}\right) \\ \\ =2\sin \left(29^{\circ \:}\right) \end{gathered}[/tex]
b)
[tex]\begin{gathered} \sec\left(\theta\right)-\text{ cosec\lparen90- }\theta) \\ \\ =\sec \left(θ\right)-\frac{1}{\cos \left(θ\right)} \\ \\ \mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cos \left(x\right)}=\sec \left(x\right) \\ \\ =\sec \left(θ\right)-\sec \left(θ\right) \\ \\ \mathrm{Add\:similar\:elements:}\:\sec \left(θ\right)-\sec \left(θ\right)=0 \\ 0 \end{gathered}[/tex]
