Question

cot theta/1-sin theta +1-sin theta /cos theta = 2 sec theta​

Answer 1

Answer:

Explanation:-

To Prove

$\mathsf{\dfrac{cosA}{1-sinA}+ \dfrac{1-sinA}{cosA} = 2 secA}$

Solution

LHS

$\mathsf{ = \dfrac{cosA}{1-sinA}+ \dfrac{1-sinA}{cosA} }$

$\mathsf{ = \dfrac{{cos}^{2}A+{(1-sinA)}^{2}}{cosA (1-sinA)} }$

$\mathsf{ = \dfrac{{cos}^{2}A+{sin}^{2}A+1-2sinA}{cosA (1-sinA)} }$

$\mathsf{ = \dfrac{1+1-2sinA}{cosA (1-sinA)} }$

$\mathsf{ = \dfrac{2-2sinA}{cosA (1-sinA)} }$

$\mathsf{ = \dfrac{2 \cancel{(1-sinA)}}{cosA \cancel {(1-sinA)}} }$

$\mathsf{ = \dfrac{2}{cosA } }$

$\mathsf{ = 2 secA}$

RHS

$\mathsf{ = 2 secA}$

LHS = RHS

Hence Proved

Answer 2

Answer:

Hey mate please refer to the attachment