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Trigonometric Ratio(sin,cos,tan)

how to simpli...

Question

how to simplify (sinAcosB+cosAsinB)/(cosAcosB-sinAsinB) to (tanA+tanB)/(1-tanAtanB)?

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A = B = 60^{\circ}

, verify that
(i)

cos (A - B) = cos A cos B + sin A sin B

sin (A - B) = sin A cos B - cos A sin B

tan (A - B) = \frac{tan A - tan B}{1 + tan A tan B}

tan A = 1

tan B = \sqrt{3},

sin A cos B + cos A sin B

tan A = 1

tan B = \sqrt{3}

cos A cos B - sin A sin B

(i)

tan (A + B) = \frac{tan A + tan B}{1 - tan A tan B}

tan 75^{\circ}

A = 45^{\circ}, B = 30^{\circ}

(i i)

cos (A - B) = cos A cos B + sin A sin B

cos 15^{\circ}

A = 45^{\circ}, B = 30^{\circ}

If cos (A-B) = $\frac{3}{5}$ and tanAtanB = 2,then

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