# Thread: Need help verifying trig equations.

1. ## Need help verifying trig equations.

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)

2. Originally Posted by BennyM
How would I verify questions, such as..

sin x = sin (360° +x)
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?

cotA * sec˛A * sin˛A = tan A
Consider the LHS

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?

(1 + sinA * cosA) (sinA - cosA) = sinłA - cosłA
Consider the RHS

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?

cscA = (secA + tanA) / (secA - cosA + tanA)
Consider the right hand side

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?