Answer:
prove [1 + cos ( 2 θ ) ]/ 2cos ( θ ) = cos ( θ ) is an identity
[ 1 + cos ( 2 θ ) ] / 2cos ( θ )
cos (2θ) = 2(cos θ)^2 - 1
so plug 2(cos θ)^2 - 1 in for cos (2 theta)
[ 1 + 2(cos θ)^2 - 1 ] / 2cos ( θ )
= [ 2(cos θ)^2 ] / 2cos ( θ )
= [ (cos θ)^2 ] / cos ( θ )
= (cos θ )
so (cos θ ) = (cos θ ) is true. Proven .
Step-by-step explanation:
prove [1 + cos ( 2 θ ) ]/ 2cos ( θ ) = cos ( θ ) is an identity
...
we need to show that the expression on the left side will eventually transform into cos (Θ)
Start with [1 + cos ( 2 θ )] / 2 cos ( θ )
prove [1 + cos ( 2 θ ) ]/ 2cos ( θ ) = cos ( θ ) is an identity
[ 1 + cos ( 2 θ ) ] / 2cos ( θ )
cos (2θ) = 2(cos θ)^2 - 1
so plug 2(cos θ)^2 - 1 in for cos (2 theta)
[ 1 + 2(cos θ)^2 - 1 ] / 2cos ( θ )
= [ 2(cos θ)^2 ] / 2cos ( θ )
= [ (cos θ)^2 ] / cos ( θ )
= (cos θ )
so (cos θ ) = (cos θ ) is true. Proven .
