What is costheta-tantheta*sectheta cosθ−tanθ⋅secθ in terms of sintheta sinθ?

1 Answer
Karthik G
Jan 9, 2016

=((1-sin^2(theta))sqrt(1-sin^2(theta)) - sin(theta))/(1-sin^2(theta))=(1−sin2(θ))√1−sin2(θ)−sin(θ)1−sin2(θ)

Explanation:

cos(theta) - tan(theta)*sec(theta)cos(θ)−tan(θ)⋅sec(θ)

=cos(theta) - sin(theta)/cos(theta) * 1/cos(theta)=cos(θ)−sin(θ)cos(θ)⋅1cos(θ)

=cos(theta) -sin(theta)/cos^2(theta)=cos(θ)−sin(θ)cos2(θ)

=sqrt(1-sin^2(theta)) - sin(theta)/(1-sin^2(theta))=√1−sin2(θ)−sin(θ)1−sin2(θ)

=((1-sin^2(theta))sqrt(1-sin^2(theta)) - sin(theta))/(1-sin^2(theta))=(1−sin2(θ))√1−sin2(θ)−sin(θ)1−sin2(θ)

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