Question

Hello, I need help solving question 9 a please, thanks

Answer 1

9

a)

`\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}`

b)

`\begin{gathered} \sec\left(\theta\right)-\text{ cosec\lparen90- }\theta) \\ \\ =\sec \left(θ\right)-(1)/(\cos \left(θ\right)) \\ \\ \mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad (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}`