Can anyone help me verify the following trig identity:
$(1-\cos A)(1+\sec A)(\cot A)= \sin A.$
My work so far is
$(1-\cos A)\left(1+\frac{1}{\cos A}\right)\frac{\cos A}{\sin A}=\sin A$
But I am stuck around this part.
Can anyone help me verify the following trig identity:
$(1-\cos A)(1+\sec A)(\cot A)= \sin A.$
My work so far is
$(1-\cos A)\left(1+\frac{1}{\cos A}\right)\frac{\cos A}{\sin A}=\sin A$
But I am stuck around this part.
Express everything on the left in terms of sines and cosines. We get $(1-\cos A) \left(1+\frac{1}{\cos A}\right)\frac{\cos A}{\sin A}.$
First multiply $1+\frac{1}{\cos A}$ by the $\cos A$ in $\frac{\cos A}{\sin A}$. We get $\cos A+1$.Our expression is now equal to $(1-\cos A)(\cos A+1)\frac{1}{\sin A}.$ But $(1-\cos A)(\cos A+1)=(1-\cos A)(1+\cos A)=1-\cos ^2 A=\sin^2 A$. Now multiply by the $\frac{1}{\sin A}$. We get $\sin A$.