Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Before solving, we should know –
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 1-sin^2x = cos^2x[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf a^2-b^2 = (a+b)(a-b)[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \dfrac{sinx}{cosx} = tanx[/tex]
__________________________________________
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\sf \dfrac{cosx}{1-sinx} -\dfrac{cosx}{1+sinx}}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \dfrac{cosx(1+sinx)-cosx(1-sinx)}{(1+sinx)(1-sinx)}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \dfrac{cosx(1+sinx-1+sinx)}{1^2-sin^2x}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \dfrac{cosx(\cancel{1}+sinx-\cancel{1}+sinx)}{cos^2x}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \dfrac{\cancel{cosx}\times 2sinx}{\cancel{cos^2x}}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \dfrac{2sinx}{cosx}[/tex]
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf 2tanx} [/tex]
- Henceforth, correct option is C.
The simplified form of the given expression is 2tanx. Option C is correct.
Trigonometry identity
Given the following trigonometry identity:
[tex]\frac{cosx}{1-sinx} -\frac{cosx}{1+sinx} [/tex]
Simplify the expression
Find the LCM of the expression to have:
[tex]=\frac{cosx}{1-sinx} -\frac{cosx}{1+sinx} \\ =\frac{cosx(1+sinx)-(cosx(1-sinx)}{(1-sinx)(1+sinx)} \\ =\frac{cosx+cosxsinx-cosx+cosxsinx}{1-sin^2x}\\ =\frac{2cosxsins}{cos^2x } \\ =\frac{2cosxsinx}{cos^2x}\\ [/tex]
This can be simplified further to have:
[tex]=\frac{2sinxcosx}{cos^2x}\\ =\frac{2sinx}{cosx}\\ =2tanx[/tex]
Therefore the simplified form of the given expression is 2tanx.
Learn more on trigonometry function here: https://brainly.com/question/4515552
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.