True or false?

Question

True or False and steps to prove. 

Question 1) tan(x)cos(x)sin(-x) = 1

Question 2) (tan(x) + sec(x))(sec(x) - tan(x)) = -1

Question 3) 5 + tan2(x) = 4 + sec2(x)

 

Answer 1

3) True 5+tan^2x = 4 + sec^2x

subtract 4 from both sides

1 +tanx^2x = sec^2x is a trig identity

1 + sin^2x/cos^2x = 1/cos^2x multiply by cos^2x to get

cos^2x + sin^2x = 1 a more familiar trig identity

2) (tanx + secx)(secx - tanx) = -1

sec^2x -tan^2x = -1

1+tan^2x -tan^2x = -1

1 = -1 False

1) False

tanxcosxsin(-x)= 1

sinx/cosx)cosxsin(-x) = sinxsin(-x) = -sin^2x = 1 is not true