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Anonymous

# how to prove cos x/sin x + sin x/cos x =2/sin2x?

i need help to prove this..

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- 1 decade agoFavorite Answer
Pf:

cosx / sinx + sinx / cosx

=cosx*cosx / sinx*cosx + sinx*sinx / cosx*sinx

=cos^2(x) / sinxcosx + sin^2(x) / cosxsinx

=cos^2(x) / sinxcosx + sin^2(x) / sinxcosx

=(cos^2(x) + sin^2(x)) / sinxcosx

=1 / sinxcosx

=2 / 2sinxcosx

=2 / sin2x

So cosx/sin x + sinx/cos x =2/sin2x

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- 1 decade ago
cosx/sinx +sinx/cosx = (cos^2x+sin^2x)/sinxcosx = 1/sinx.cosx

= 2/2sinxcosx = 2/sin2x

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- ThinkerLv 41 decade ago
cosx . . sinx . . .cos²x + sin²x . . . . .1 . . . . . . . . . . 1

-------- + ------- = -------------------- = -------------- = -------------------- =

sinx . . .cosx . . . sinxcosx . . . . sinxcosx . . (2sinxcosx)/2

. . . . 2 . . . . . . 2

--------------- = ---------

2sinxcosx . . sin2x

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