Determine wether each statement is true or false.

Question

1. cosx²+sinx²=1

2) csc(2x)=1/2csc(x)sec(x)

Answer 1

1) True

cos^2x + sin^2x = 1

cosx = adjacent side/hypotenuse= a/h

sinx = opposite side/hypotenuse = o/h

(a/h)^2 + (o/h)^2 = (a^2+o^2)/h^2 = 1

for a right triangle, a^2 + o^2 = h^2

h^2/h^2 = 1

2) False

IF csc2x = 1/2cscxsecx

then 1/sin2x = 2cscxsecx = 2/sinxcosx

sin2x = sinxcosx/2 but sin2x = 2sinxcosx, the 2 is in the wrong place. It's "close" but not close enough.

2sin2x = sinxcosx

2sin60 = siin30cos30

2sqr3/2 = (1/2)sqr3/2

sqr3 doesn't = sqr3/4

try x = 30 degrees

csc60 = 1/2csc30sec30

1/sin60 = (1/2)sin30cos30

1/sqr3/2 = (1/2)(1/2)sqr3/2

2/sqr3 = sqr3/8

cross multiply

3 doesn't equal 16

one counterexample disproves an "identity"