If A - B -3 and cos A -cos B -1then find the value of cos A - B -2

We have, A+B=π/3 and cosA+cosB=1 Now, CosA+cpsB=1 ⇒ cos (A+B/2 )cos (A B/2 )=1 ⇒ 2cos ( 1/2×π/3 )cos (A B/2 )=1 [ ∵ A+B=π/3 ] ⇒ 2cosπ/6cos (A B/2 )=1 ⇒ 2× ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

If A + B =π/3...

Question

If $A + B = \frac{π}{3}$ and $c o s A + c o s B = 1$
then find the value of $c o s \frac{A - B}{2}$

Open in App

Solution

We have,
$A + B = \frac{π}{3} a n d c o s A + c o s B = 1$
Now,
$C o s A + c p s B = 1 \Rightarrow c o s (\frac{A + B}{2}) c o s (\frac{A - B}{2}) = 1 \Rightarrow 2 c o s (\frac{1}{2} \times \frac{π}{3}) c o s (\frac{A - B}{2}) = 1 [∵ A + B = \frac{π}{3}] \Rightarrow 2 c o s \frac{π}{6} c o s (\frac{A - B}{2}) = 1 \Rightarrow 2 \times \frac{\sqrt{3}}{2} \times c o s (\frac{A - B}{2}) = 1 \Rightarrow \sqrt{3} c o s c o s (\frac{A - B}{2}) = 1 \Rightarrow c o s (\frac{A - B}{2}) = \frac{1}{\sqrt{3}}$
Hence, $c o s (\frac{A - B}{2}) = \frac{1}{\sqrt{3}}$

Suggest Corrections

Similar questions

Q. If

A + B = \frac{π}{3}

and

c o s A + c o s B = 1

then find the value of

cos \frac{(A - B)}{2}

Q. If

A + B = \frac{π}{3}

and

cos A + cos B = 1

then

cos (A - B)

A + B = \frac{π}{3}; cos A + cos B = 1

, value of

| cos A - cos B |

Q. If

A + B = \frac{π}{3}

and

cos A + cos B = 1

then

Q. If

cos A = \frac{3}{5}, cos B = \frac{4}{5}

and

\frac{- π}{2} < A < 0, \frac{- π}{2} < B < 0

, then the value of

2 sin A + 4 sin B =

Join BYJU'S Learning Program

If A+B=π3 and cosA+cosB=1 then find the value of cosA−B2

We have, A+B=π3andcosA+cosB=1 Now, CosA+cpsB=1⇒cos(A+B2)cos(A−B2)=1⇒2cos(12×π3)cos(A−B2)=1[∵A+B=π3]⇒2cosπ6cos(A−B2)=1⇒2×√32×cos(A−B2)=1⇒√3coscos(A−B2)=1⇒cos(A−B2)=1√3 Hence, cos(A−B2)=1√3

If $A + B = \frac{π}{3}$ and $c o s A + c o s B = 1$
then find the value of $c o s \frac{A - B}{2}$