What is tan(θ)+tan(pi/2-θ) ?

The solution to tan(θ)+tan(pi/2-θ) is 2csc(2θ)

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simplify tan(θ)+tan(pi/2-θ)

simplify

tan (θ) + tan (\frac{π}{2} - θ)

2 csc (2 θ)

Solution steps

tan (θ) + tan (\frac{π}{2} - θ)

Rewrite using trig identities

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

Express with sin, cos

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

Rewrite using trig identities

= 2 csc (2 θ)

sin (\frac{3 π}{2} + θ)

3 cos (\frac{1}{2} x + π) - 5

- cos (- A)

sin (- θ) + cos (\frac{π}{2} - θ)

sin (nπ) - sin (- nπ)