Question

What is the formula for (tanC-tanD)

Answer 1

We know that
i) tan θ = sin θ/ cosθ

ii) sin(A-B)= sinAcosB-sinBcosA
Know we have find
tan C - tan D

=(sin C/cos C ) - (sinD/ cosD)

=(sinCcosD-sinDcosC)/(cosCcosD)
=sin(C-D)/(cosCcosD

Answer 2

The formula for $\bold{(\tan C-\tan D)=\frac{\sin (C-D)}{\cos C \cos D}}$

To find:

Formula for $(\tan C-\tan D)=?$

Solution:

We know that $\tan \theta=\frac{\sin \theta}{\cos \theta}$

$\bold{\sin (A-B)=\sin A \cos B-\sin B \cos A}$

We are to find tan C - tan D. The formula for the same is as under:

$(\tan C-\tan D)$

$=\left(\frac{\sin C}{\cos C}\right)-\left(\frac{\sin D}{\cos D}\right)$

$=\frac{(\sin C \cos D-\sin D \cos C)}{(\cos C \cos D)}\quad (\text {Taking the LCM of cos C and cos D})$

$=\frac{\sin (C-D)}{\cos C \cos D}$

Therefore, $\bold{(\tan C-\tan D)=\frac{\sin (C-D)}{\cos C \cos D}}$