If ABCD is a Cyclic Quadrilateral, then the value of cos²A – cos²B – cos²C + cos²D is:

Question

Question

This question was previously asked in

RRB ALP Previous Paper 11 (Held On: 17 Aug 2018 Shift 1)

Answer 1

Calculation:

Opposite angles of a cyclic Quadrilateral are supplementary.

So,

A + C = 180°, ⇒ C = 180° - A

B + D = 180°, ⇒ D = 180 - B

Now,

cos2A – cos2B – cos2C + cos2D

⇒ cos²A – cos²B – cos²(180 - A) + cos²(180 - B)

⇒ cos2A – cos2B – {cos(180 - A)}² + {cos(180 - B)}²

⇒ cos2A – cos2B – {- cos A}2 + {- cos B}2

⇒ cos2A – cos2B – cos²A + cos²B

⇒ cos2A – cos2A – cos2B + cos2B

⇒ 0 - 0 = 0

Hence, the correct answer is option (3).

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