Simplify the trigonometric expression 5 cotA 51 tanA Simpl

Simplify the trigonometric expression. 5 cot(A) - 5/1 + tan(-A) Simplify the trigonometric expression. 3/1 - sin(alpha) + 3/1 + sin(alpha)

Solution

5(cot(A)-1)/(1+tan(-A))= 5(cotA - 1)/(1-tanA)

cot A= cosA/sinA and tanA= sinA/cos A

                             =5(cosA/sinA-1)/(1-sinA/cosA)= 5cosA(cosA-sinA)/(cosA-sinA)sinA

                                                                        =5cot A

3/(1-sin alpha) + 3/(1+sin alpha)= (3(1+sin alpha) + 3(1-sin alpha))/(1-sin^2alpha)

                                             = (6/cos^2 alpha)=6sec^2 alpha