Question

Solve it.................

Answer 1

Given:

= > (a - b)^2 cos^2 c/2 + (a + b)^2 sin^2 c/2

= > (a - b)^2 (1 - sin^2 c/2) + (a + b)^2 sin^2 c/2

= > (a - b)^2 - (a - b)^2(sin^2 c/2) + (a + b)^2 sin^2 c/2

= > (a - b)^2 + (a + b)^2 sin^2 c/2 - (a - b)^2 sin^2 c/2

= > a^2 + b^2 - 2ab + a^2 + b^2 + 2ab sin^2 c/2 - (a^2 + b^2 - 2ab) sin^2 c/2

= > a^2 + b^2 - 2ab + a^2 + b^2 + 2ab sin^2 c/2 - a^2 - b^2 + 2ab sin^2 c/2

= > a^2 + b^2 - 2ab + 4absin^2 c/2

= > a^2 + b^2 - 2ab[1 - 2sin^2 c/2]

= > a^2 + b^2 - 2ab[cos2c/2]

We know that 1 - 2sin^2 theta = cos2theta

= > a^2 + b^2 - 2ab[cosc]

= > a^2 + b^2 - 2abcosc

We know that a^2 + b^2 -2abcosc = c^2

= > c^2.


Hope this helps!

Answer 2

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