Question

if TanA=15/8 and TanB=7/24 find cosec(A-B)​

Answer 1

Answer: cosec(A-B)=1/sin(A-B)

sin(A-B)=sinAcosB-cosAsinB

if tanA=15/8 then sinA=15/17,cosA=8/17

if tanB=7/24 then sinB=7/25

sin(A-B)=(15/17)(24/25)-(8/17)(7/25)=304/425

then cosec(A-B)=1/sin(A-B)=425/304

Step-by-step explanation:

Answer 2

Answer:

$\frac{425}{304}$

Step-by-step explanation:

Given,

$\tan A=\frac{15}{8}$

$\because \tan A =\frac{\text{opposite leg}}{\text{Adjacent leg}}$

Now,

$\sin A = \frac{\text{opposite leg}}{\tex{Hypotenuse}}$

$=\frac{15}{\sqrt{15^2+8^2}}$

$=\frac{15}{\sqrt{225+64}}$

$=\frac{15}{\sqrt{289}}$

$=\frac{15}{17}$

$\cos A = \frac{\text{adjacent leg}}{\text{hypotenuse}}=\frac{8}{17}$

Similarly,

$\tan B=\frac{7}{24}$

$\implies\sin B=\frac{7}{\sqrt{7^2+24^2}}$

$=\frac{7}{\sqrt{49+576}}$

$=\frac{7}{\sqrt{625}}$

$=\frac{7}{25}$

$\cos B=\frac{24}{25}$

$cosec (A-B)=\frac{1}{sin (A-B)}=\frac{1}{sin A cos B - sin B cos A}$

$=\frac{1}{\frac{15}{17}\times \frac{24}{25}-\frac{7}{25}\times \frac{8}{17}}$

$=\frac{17\times 25}{360-56}$

$=\frac{425}{304}$