Question

if tan A =15/8 and tan B =7/24, then cos a-b=​

Answer 1

Answer:

Step-by-step explanation:

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 cos (A-B)=1/sin(A-B)=425/304

Answer 2

Answer:

\frac{425}{304}

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:

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}