trigonometry equations

[fiery123]

Evaluate
[tan(180+x)]/[sin(180-x)] times [tan(90+x)]/[cos^2(180+x)] times sin(-x) - 1

=(tanx)/(sinx) times (-tanx)/[cos^2(x)] times -sinx - 1

= 1/cosx times -sinx/cos^3(x) times -sinx -1

=sin^2(x)/cos^4(x) - 1

im stuck at this point can someone help me out.

[krtxmrtz]

Evaluating each factor separately:

tan(180 + x)/sin(180 + x) = tan(x)/sin(x) = 1/cos(x)

tan(90 + x)/cos²(180 + x) = (-1/tan(x)) / cos²(x)

sin(-x) = -sin(x)

Grouping all factors you get:

(1/cos(x))*(1/-tan(x))*(-sin(x)/cos²(x)) - 1 =

1/cos²(x) - 1 = tan²(x)

[fiery123]

right thank you very much

[krtxmrtz]

right thank you very much

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