If cos A-cos B-12 and sin A-sin B-14Prove that tan A-B2-12

cos A +cos B = 1 2 sin A +sin B = 1 4 2cos( A+B 2 #160; ) #160; cos( A B 2 #160; ) #160; = 1 2 → 1 2sin( A+B 2 #160 ...

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Byju's Answer

Standard XII

Mathematics

Sin(A+B)Sin(A-B)

If cos A+co...

Question

If $cos A + cos B = \frac{1}{2}$ and $sin A + sin B = \frac{1}{4}$
Prove that $\frac{tan (A + B)}{2} = \frac{1}{2}$

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Solution

$cos A + cos B = \frac{1}{2} sin A + sin B = \frac{1}{4}$
$2 cos (\frac{A + B}{2}) cos (\frac{A - B}{2}) = \frac{1}{2} \to 12 sin (\frac{A + B}{2}) cos (\frac{A - B}{2}) = \frac{1}{4} \to 2$
$2 / 1$
$∴ tan (\frac{A + B}{2}) = \frac{1}{4} \times 2 = \frac{1}{2}$
$∴ tan (\frac{A + B}{2}) = \frac{1}{2}$

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If cosA+cosB=12 and sinA+sinB=14Prove that tan(A+B)2=12

cosA+cosB=12sinA+sinB=142cos(A+B2)cos(A−B2)=12→12sin(A+B2)cos(A−B2)=14→22/1∴tan(A+B2)=14×2=12∴tan(A+B2)=12

If $cos A + cos B = \frac{1}{2}$ and $sin A + sin B = \frac{1}{4}$
Prove that $\frac{tan (A + B)}{2} = \frac{1}{2}$