Question

if A=B=60°verify that cos(A-B)= cos A cos B + sin A sin B

Answer 1

Answer:

here,

A = B = 60°

LHS,

cos(A - B) = cos( 60 -60) = cos0° = 1.

now, Rhs

cosAcosB + sinAsinB

= cos60 × cos60 + sin60× sin60

=

$(\frac{1}{2} \times \frac{1}{2} ) + ( \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} ) \\ = \frac{1}{4} + \frac{3}{4} \\ = \frac{1 + 3}{4} \\ = \frac{4}{4} \\ = 1.$

so,

LHS = RHS = 1.

HENCE PROVED.

Step-by-step explanation:

some trigonometric values:

cos0° = 1

cos60° = ½

sin60° = √3/2

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