Question

If x cos A + y sin A = x cos B + y sin B = k ,show that x*(1/2 (A + B)) = sin*(1/2 * (A + B)) = cos* (1/2 * (A - B))​

Answer 1

Step-by-step explanation:

that

dx

dy

=

sina

cos

2

(a+y)

Medium

Solution

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We have, cosy=xcos(a+y)→(1)

Differentiate both sides w.r.t. x

−siny

dx

dy

=cos(a+y)−xsin(a+y)

dx

dy

⇒

dx

dy

=

xsin(a+y)−siny

cos(a+y)

=

cos(a+y)

cosy

sin(a+y)−siny

cos(a+y)

=

cosysin(a+y)−sinycos(a+y)

cos

2

(a+y)

=

sina

cos

2

(a+y)

Since sin(A−B)=sinAcosB−sinBcosA

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