Verify the identity. (7\cos x-\sin x)^2+(\cos x+7\sin x)^2=50

Jerold

Jerold

Answered question

2021-09-16

Verify the identity
(7cosxsinx)2+(cosx+7sinx)2=50

Answer & Explanation

Nichole Watt

Nichole Watt

Skilled2021-09-17Added 100 answers

Given,
(7cosxsinx)2+(cosx+7sinx)2=50
Left-hand side
(7cosxsinx)2+(cosx+7sinx)2
=49cosx+sin2x2(7)cosxsinx+cos2x+49sin2x+2(7)cosxsinx
=49cos2x+49sin2x+sin2x+cos2x
=49(cos2x+sin2x)+(sin2x+cos2x)
=(49+1)(sin2x+cos2x)
=50(sin2x+cos2x)
Using the first identity of trigonometry
sin2x+cos2x=1
Then
=50(sin2x+cos2x)
=50(1)
=50
=RHS
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-11Added 2605 answers

Answer is given below (on video)

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