UESTION 4 1 Given the following expression: (sinx)/(1+cosx)+(cosx)/(sinx) 4.4.1 Prove that: (sinx)/(1+cosx)+(cosx)/(sinx)=(1)/(sinx) 4.4.2 Determine the general solution for which the identity in QUESTION 4.4.1 is undefined. CAPS - Grade 11 If 2cosbeta +1=0 and sinbeta lt 0 determine WITHOUT the use of a calculator and with the aid of a diagram, the value of: 4.1.1 sinbeta 4.1.2 2tan^2beta -cos^2beta 4.2 Simplify (cos(Theta -90^circ )cdot cos(-Theta )cdot tan(360^circ -Theta ))/(sin(180^circ )+Theta ) to a single trigonometric term. 4.3 WITHOUT using a calculator calculate the value of: (2sin510^circ -cos340^circ cdot cos20^circ )/(cos^2)110^(circ ) 4.4

4.4.1 To prove that , let's start by finding a common denominator for the two fractions on the left side of the equation. The common denominator is . Multiplying the numerator and denominator of each fraction by this common denominator, we get: Expanding the numerator, we have: Using the Pythagorean identity , we can simplify the numerator further: Canceling out the common factor of in the numerator and denominator, we are left with: Therefore, we have proven that .4.4.2 The identity is undefined when the denominator is equal to zero. This occurs when . The general solution for is , where is an integer.4.1.1 Given that and , we can solve for by rearranging the equation: Since , we know that is in the third or fourth quadrant. In the third quadrant, both sine and cosine are negative, while in the fourth quadrant, only cosine is positive. Therefore, must be in the third quadrant.The reference angle for is or . Since is in the third quadrant, the general solution for is: where is an integer.4.1.2 To find the value of , we can use the identity and the fact that .Since , we can find using the Pythagorean identity: Since is in the third quadrant, is negative. Therefore, .Now, we can find : Finally, we can find : 4.2 To simplify $\frac {cos(\Theta -90^{\circ })\cdot cos(-\Theta )\cdot tan(360^{\circ }-\Theta