If cos A-mcos B- then write the value of A-B-2A-B-2

We have. cosA=mcosB, cosA/cosB=m ⇒cosA/cosB+1=m+1 ⇒cosA+cosB/cosB=m+1 …(i) Again, cosA/cosB=m ⇒cosA/cosB 1=m 1 ⇒cosA cosB/cosB=m 1…(ii) Dividing equation (i ...

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Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

If cos A=mcos...

Question

If $c o s A = m c o s B$ , then write the value of $c o t \frac{A + B}{2} c o t \frac{A - B}{2}$

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Solution

We have.
$c o s A = m c o s B, \frac{c o s A}{c o s B} = m \Rightarrow \frac{c o s A}{c o s B} + 1 = m + 1 \Rightarrow \frac{c o s A + c o s B}{c o s B} = m + 1 \dots (i)$
Again,
$\frac{c o s A}{c o s B} = m \Rightarrow \frac{c o s A}{c o s B} - 1 = m - 1 \Rightarrow \frac{c o s A - c o s B}{c o s B} = m - 1 \dots (i i)$
Dividing equation (i) by equation (ii), we get
$cosA+cosBcosBcosA−cosBcosB=m−1m−1⇒cosA+cosBcsosA−cosB=fracm−1m−1⇒2cos(A+B2)cos(A−B2)2sin(A+B2)sin(A−B2)=m+1m−1⇒−cot(A+B2)cot(A−B2)=m+1m−1⇒cot(A+B2)cot(A−B2)=1+m1−m∴cot(A+B2)cot(A−B2)=1+m1−m$

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