Write the trigonometric expression in terms of sine and cosine, and then simplify.

Question

1). (csc θ − sin θ)/(cos θ)

____________.

2). Simplify the trigonometric expression.

(cos u + 1)/(sin u) +
(sin u)/(1 + cos u)

______________.

Answer 1

(csc θ − sin θ)/(cos θ)
(1/sin- sin^2/sin)/cos

(1-sin^2)*sin/cos
cos^2*sin/cos
cos*sin

:(cos+1)/sin + sin/(1+cosu)

common denominaator:sin(1+cos)

1+2cos+cos^2 + sin^2 all over denominator

2(1+cos)/sin(1+cos)

2/sinU
check that.

Answer 2

(csc θ − sin θ)/(cos θ)
= (1/sinθ - sinθ)/cosθ
= (1-sin^2θ)/(sinθ cosθ)
= cos^2θ/(sinθ cosθ)
= cosθ/sinθ
= cotθ