If sin A-B - 1 and sin A-B - 1 - 3 - find the value of tan A - tan B-

sin(A+B)=1 A+B=π/2 A=π/2 B sin(A B)=1√(3)sin (π/2 2B)=1√(3)cos 2B=1√(3)sin 2B=√(23) sin 2B=√(23)2tan B1+tan^2 B=√(23) 1+tan^2 Btan B=√(6) B+ ...

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Standard XII

Mathematics

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

If sin A+B ...

Question

If $sin (A + B)$ = 1 and sin (A-B) = $\frac{1}{\sqrt{3}}$ , find the value of $tan A + tan B$ .

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Solution

$sin (A + B) = 1 ⟹ A + B = π / 2 ⟹ A = π / 2 - B$
$sin (A - B) = \frac{1}{\sqrt{3}} ⟹ sin (π / 2 - 2 B) = \frac{1}{\sqrt{3}} ⟹ cos 2 B = \frac{1}{\sqrt{3}} ⟹ sin 2 B = \sqrt{\frac{2}{3}}$
$sin 2 B = \sqrt{\frac{2}{3}} ⟹ \frac{2 tan B}{1 + {tan}^{2} B} = \sqrt{\frac{2}{3}}$
$⟹ \frac{1 + {tan}^{2} B}{tan B} = \sqrt{6} ⟹ cot B + tan B = \sqrt{6} ⟹ cot (π / 2 - A) + tan B = \sqrt{6}$
$⟹ tan A + tan B = \sqrt{6}$

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If sin(A+B) = 1 and sin (A-B) = 1√3, find the value of tanA+tanB.

sin(A+B)=1⟹A+B=π/2⟹A=π/2−Bsin(A−B)=1√3⟹sin(π/2−2B)=1√3⟹cos2B=1√3⟹sin2B=√23sin2B=√23⟹2tanB1+tan2B=√23⟹1+tan2BtanB=√6⟹cotB+tanB=√6⟹cot(π/2−A)+tanB=√6⟹tanA+tanB=√6

If $sin (A + B)$ = 1 and sin (A-B) = $\frac{1}{\sqrt{3}}$ , find the value of $tan A + tan B$ .