Question

Hello, I need help simplifying question 16 i please, thanks

Answer 1

Given -

i. 5cot²θ + 5

To Find -

Simplification =?

Step-by-Step Explanation -

We know that

`cot\theta\text{ = }(\cos\theta)/(\sin\theta)`

So, simply putting it in the given equation:

`\begin{gathered} =\text{ }5(\cos^2\theta)/(\sin^2\theta)\text{ + 5 } \\ \\ =\text{ 5}(\lparen\cos^2\theta+\sin^2\theta\rparen)/(\sin^2\theta) \\ \\ We\text{ know taht }\sin^2\theta\text{ + }\cos^2\text{ = 1} \\ \\ So,\text{ } \\ \\ =\text{ }(5)/(\sin^2\theta) \end{gathered}`

Final Answer -

= 5/sin²θ