Is tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ)) ?

The answer to whether tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ)) is True

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prove tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ))

prove

tan (\frac{π}{4} - θ) = \frac{cos ( θ ) - sin ( θ )}{cos ( θ ) + sin ( θ )}

True

Solution steps

tan (\frac{π}{4} - θ) = \frac{cos ( θ ) - sin ( θ )}{cos ( θ ) + sin ( θ )}

Manipulating left side

tan (\frac{π}{4} - θ)

Rewrite using trig identities

= \frac{cos ( θ ) - sin ( θ )}{cos ( θ ) + sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

2 cos^{2} (x) + sin^{2} (x) = 1 + cos^{2} (x)

\frac{1 + sec ^{2} ( θ )}{sec ^{2} ( θ )} = 1 + cos^{2} (θ)

cos (2 a + a) = - 3 cos (a) + 4 cos^{3} (a)

csc^{2} (θ) - cos (θ) sec (θ) = cot^{2} (θ)

sin (x) + cos (x) = 1

Is tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ)) ?
The answer to whether tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ)) is True