sin 2A/1+cos2A=tanA prove it
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Answered by
89
sin2A/1+cos2A
= (2sinAcosA)/(1+2cos^(2)A-1)
=(2sinAcosA)/ cos^(2)A
= 2sinA/cosA
=2tanA
= (2sinAcosA)/(1+2cos^(2)A-1)
=(2sinAcosA)/ cos^(2)A
= 2sinA/cosA
=2tanA
800Neerajkumar11:
very intelligent done
I think the 3rd step should be (2sinAcosA)/2cos^(2)A
oh yaah...thats mistake....and then 2 also canceled out and thats will be right
Answered by
63
Given sin 2A/1 + cos 2A. ------ (1)
We know that sin 2 theta = 2 sin theta cos theta
sin 2 A = 2 sin A cos A ------ (2).
We know that cos 2 theta = 2 cos^2 x - 1
cos 2 A = 2 cos^2 A - 1 --------- (3).
Substitute (2) & (3) in (1), we get
2 sin A cos A/1 + 2 cos^2A - 1
2 sin A cos A/2 cos^2 A
2 sin A cos A/ 2 * cos A * cos A
sin A/cos A
tan A.
Hope this helps!
We know that sin 2 theta = 2 sin theta cos theta
sin 2 A = 2 sin A cos A ------ (2).
We know that cos 2 theta = 2 cos^2 x - 1
cos 2 A = 2 cos^2 A - 1 --------- (3).
Substitute (2) & (3) in (1), we get
2 sin A cos A/1 + 2 cos^2A - 1
2 sin A cos A/2 cos^2 A
2 sin A cos A/ 2 * cos A * cos A
sin A/cos A
tan A.
Hope this helps!
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