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Question: If the coordinates of vertices of \(\Delta OAB\) are (0,0) \((\cos\alpha,\sin\alpha)\) and \(( - \si...

If the coordinates of vertices of ΔOAB\Delta OAB are (0,0) (cos⁡α,sin⁡α)(\cos\alpha,\sin\alpha) and (−sin⁡α,cos⁡α)( - \sin\alpha,\cos\alpha) respectively, then

OA2+OB2=OA^{2} + OB^{2} =

A

0

B

1

C

2

D

3

Answer

2

Explanation

Solution

OA2=cos⁡2α+sin⁡2α=1O A ^ { 2 } = \cos ^ { 2 } \alpha + \sin ^ { 2 } \alpha = 1

and OB2=sin⁡2α+cos⁡2α=1O B ^ { 2 } = \sin ^ { 2 } \alpha + \cos ^ { 2 } \alpha = 1.

Hence OA2+OB2=1+1=2O A ^ { 2 } + O B ^ { 2 } = 1 + 1 = 2.