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Implicit Differentiation

Prove that:- ...

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Prove that:- 1) Sin (A+B) =sinAcosB+cosAsinB 2) Sin(A-B) =sinAcosB-cosAsinB 3) Cos(A-B) =cosAcosB+sinAsinB 4) Cos(A+B) =cosAcosB-sinAsinB

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A = 30^{\circ}

B = 60^{\circ}

, verify that
(i)

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

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

Q. If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.

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}

Q. If A = B = 45°, verify that:
(i) sin (A + B) = sin A cos B + cos A sin B
(ii) sin (A − B) = sin A cos B − cos A sin B
(iii) cos (A + B) = cos A cos B − sin A sin B
(iv) cos (A − B) = cos A cos B + sin A sin B

If sin(A - B) = sinA cos B - cosA sinB and cos(A - B)= cos A cos B + sin Asin B then find
sin15 and cos 15 .

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