Question

prove that :(cosx+cosy)^2+(sinx-siny)^2 =4cos^2(x+y)/2​

Answer 1

Answer:

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Answer 2

Answer:

4cos^2(x + y)/2​

Step-by-step explanation:

LHS:-

(cos x + cos y)^2+( sin x - sin y)^2

put the formula

(a + b)^2 + ( a + b)^2

=  [2 cos(x + y/2) . cos(x - y /2) ]^2 + [2 cos(x + y/2) . sin(x - y /2) ]^2

=  4.cos ^2 (x + y/2) . cos ^2 (x - y /2) + 4.cos ^2 (x + y/2) . sin ^2 (x - y /2)

take common

 4.cos ^2 (x + y/2)

=  4.cos ^2 (x + y/2) [ cos ^2  (x - y /2) + sin ^2 (x - y /2) ]

we know that ,

                         sin ^2 ∅ + cos ^2 ∅ = 1

                               ∅ = x - y / 2

Therefore,

                      4cos^2( x + y )/2​

                                                           LHS = RHS...