Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x)

Question

1.A.SIMPLIFY sin(x-360)sin(90-x)tan(-x)/cos(90+x) to a single trigonometric ratio
B.hence or otherwise without using a calculator,solve for X if 0<X<360.
sin(x-360)sin(90-x)tan(-x)/cos(90+x) =0,5

2.A.prove that 8/sin^2A - 4/1+cosA=4/1-cosA
B. For which value(s) of A in the interval 0<A<360 is the identity in question 2.A
undefined?

Answer 1

sin(x-360)sin(90-x)tan(-x)/cos(90+x)
= sin(x)cos(x)(-sin(x)/cos(x))/(-sin(x))
= sin(x)
x = 30

8/sin^2A - 4/1+cosA
8/(1-cos^2A) - 4/(1+cosA)
(8 - 4(1-cosA))/(1-cos^2A)
(8-4+4cosA)/(1-cos^2A)
4(1+cosA)/(1-cos^2A)
4/(1-cosA)

undefined when cosA = 1
So, on 0<A<360 it is defined everywhere.

Answer 2

ThanQ steve