Question

Show that : sin(45+A) sin (45-A) = 1/2 cos2A.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution:

LHS = sin(45+A)sin(45-A)

= sin[90-(45-A)]sin(45-A)

= cos(45-A)sin(45-A)

\* By complementary angles:

sin(90-A) = cosA */

= $\frac{1}{2}\times 2sin(45-A)cos(45-A)$

= $\frac{1}{2}\times sin[2(45-A)]$

/* 2sinAcosA = sin2A */

= $\frac{1}{2}sin(90-2A)$

= $\frac{1}{2}cos2A$

/* sin(90-A) = cosA */

= RHS

Therefore,

sin(45+A) sin (45-A)

= 1/2 cos2A

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