Question

tan θ/(sec θ − cos θ)

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

Answer 1

(sin θ/cos θ)/(1/cos θ)-cos θ is what I have in terms of sin and cosine, I'm not really sure how to simplify this.

Answer 2

(sinθ/cosθ)cosθ-cosθ =sinθ-cosθ

Answer 3

The final answer should be csc θ. There is a division sign inbetween the (sin θ/cos θ) and (1/cos θ) - cos θ.

Answer 4

ahh, so it's: tan θ/(sec θ − cos θ) ?

Answer 5

Is your question this
tanx/(secx-cosx)

Answer 6

yea
sorry i didnt put the parenthesis in the original question.

Answer 7

sec θ − cos θ = 1/cos θ -cos θ =(1- cos^2 θ)/cos θ = sin^2θ/cos θ
Now: tanθ /sin^2θ/cos θ=( sinθ/cosθ)(cosθ /sin^2θ) =1/sinθ= coscθ

Answer 8

sinx/cosx((1/cosx)-cosx)
=sinx/cosx((1-cos^2x)/cosx)
=sinx/sin^2x
=1/sinx
=cosecx
1-cos^2x=sin^2x
This is derived from
sin^2x+cos^2x=1

Answer 9

\[(\sin \theta /\cos \theta)/((1/\cos \theta)-\cos \theta)\]
on simplification
\[\sin \theta/1-\cos^2\theta\]
\[\sin \theta/\sin^2\theta\]

\[1/\sin \theta\]
\[cosec \theta\]