MathsSs triG

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

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?

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  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.

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  2. ThanQ steve

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