How would I verify questions, such as..
sin x = sin (360° +x)
cotA * sec˛A * sin˛A = tan A
(1 + sinA * cosA) (sinA - cosA) = sinłA - cosłA
cscA = (secA + tanA) / (secA - cosA + tanA)
Consider the RHS
and use the addition formula for sine
$\displaystyle \sin (A + B) = \sin A \cos B + \sin B \cos A$
can you continue?
Consider the LHScotA * sec˛A * sin˛A = tan A
change $\displaystyle \cot A$ to $\displaystyle \frac {\cos A}{\sin A}$
change $\displaystyle \sec^2 A$ to $\displaystyle \frac 1{\cos^2 A}$
can you continue?
Consider the RHS
(1 + sinA * cosA) (sinA - cosA) = sinłA - cosłA
use the formula for the difference of two cubes on $\displaystyle \sin^3 A - \cos^3 A$ to expand it
difference of two cubes formula: $\displaystyle a^3 - b^3 = (a - b) \left( a^2 + ab + b^2 \right)$
can you continue?
Consider the right hand sidecscA = (secA + tanA) / (secA - cosA + tanA)
change $\displaystyle \sec A$ to $\displaystyle \frac 1{\cos A}$
change $\displaystyle \tan A$ to $\displaystyle \frac {\sin A}{\cos A}$
then combine all the fractions and simplify as much as possible
can you continue?