Convert the first trigonometric expression to the second expression.
You need to learn to use parenthesis to group operations - so that your problems make sense
1. cot Y/(csc Y+1) ; (csc Y-1)/cot Y
\(\displaystyle \frac{\cot (y)}{\csc (y) + 1}\)
\(\displaystyle = \, \frac{\cot (y)}{\csc (y) + 1} \cdot \frac{\csc (y) - 1}{\csc (y) - 1}\)
\(\displaystyle = \, \frac{\cot (y)\cdot {[\csc (y) - 1]}}{\csc ^2(y) - 1}\)
Now continue....
2. sec X + csc X - cos X - sin X ; sin X tan X + cos X cot X
\(\displaystyle = \, \sec (x) - \cos (x) + \csc (x) - \sin (x)\)
\(\displaystyle = \, \frac{1}{\cos (x)} - \cos (x) + \frac{1}{\sin (x)} - \sin (x)\)
\(\displaystyle = \, \frac{1 \, - \cos ^2(x)}{\cos (x)} + \frac{1 \,- \sin^2 (x)}{\sin (x)}\)
Now continue....
3. cos^2 B + 26 cos B + 169/cos^2 B - 169 ; cos B + 13/cos B - 13
Group your operations using parenthesis
then use
\(\displaystyle (a \, + \, b)^2 \, = \, a^2 \, + \, 2\cdot a \cdot b \, + \, b^2\)
and
\(\displaystyle a^2 \, - \, b^2 \, = \, (a \, + \, b)\cdot (a \, - \, b)\)
and
\(\displaystyle 13^2 \, = \, 169\)
