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# how do you prove these trigonometry question?

sinθ(cscθ-sinθ)=cos^2θ

sinθcosθ+sinθ/cosθ+cos^θ=tanθ

they look easy....but then i tried to solve them...-_-

i seriously do not understand it!please help!

Thank you!

Update:

sinθcosθ+sinθ/cosθ+cos^2θ=tanθ

### 2 Answers

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- ---Lv 68 years agoFavorite Answer
LHS

=sinθ(1/sinθ-sinθ)

=1-sin^2θ --- since sin^2θ+cos^2θ=1

=cos^2θ

=RHS

LHS

=sinθ(cosθ+1)/cosθ(1+cosθ)

=sinθ/cosθ

=tanθ

=RHS

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- Anonymous8 years ago
Part 1 is quite simple realty:

Sinx(cosecx - sinx) = 1 - sin^2x .... Cosecx = 1/sinx

= cos^2x ..... Sin^2x + cos^2x = 1

Is something missing in the next question?

The proper question should be (sinx cosx+sinx)/(cosx+cos^2x)=tanx ... Factor the numerator and factor the denominator and you will be left with sinx/cosx which is tanx

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