Question #352ac

2 Answers
Feb 16, 2018

tan (theta) tan(θ)

Explanation:

sec(theta) -= 1/cos(theta) sec(θ)1cos(θ)

=> sin(theta)sec(theta) -= sin(theta)*1/cos(theta)sin(θ)sec(θ)sin(θ)1cos(θ)

=sin(theta)/cos(theta)=sin(θ)cos(θ)

=tan(theta)=tan(θ)

Feb 16, 2018

tan(theta)=sin(theta)sec(theta)tan(θ)=sin(θ)sec(θ)

Explanation:

sec(theta)sec(θ) is another way of writing 1/cos(theta)1cos(θ)

So sin(theta)xxsec(theta) = sin(theta)xx1/cos(theta) = sin(theta)/cos(theta)sin(θ)×sec(θ)=sin(θ)×1cos(θ)=sin(θ)cos(θ)

but we also have tan(theta)=sin(theta)/cos(theta)tan(θ)=sin(θ)cos(θ)

Thus tan(theta)=sin(theta)sec(theta)tan(θ)=sin(θ)sec(θ)