# Trigonometry

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#1
Could someone help with the following question?
Solve thefollowing in the interval -180° to 180°.
sinx ( cosx plus cosecx ) = 2cos^2 x

You don't have to give the solutions but just simplify the equation for me. I got as far as -cos^2 x plus sinxcosx plus sin^2 x. I just want to eliminate either cos or sin from the equation
Last edited by SeverusESnape; 1 year ago
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1 year ago
#2
(Original post by SeverusESnape)
Could someone help with the following question?
Solve thefollowing in the interval -180° to 180°.
sinx ( cosx + cosecx ) = 2cos^2 x

You don't have to give the solutions but just simplify the equation for me. I got as far as cos^2 x + sinxcosx - sin^2 x. I just want to eliminate either cos or sin from the equation
Could you post your working so far?
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1 year ago
#3
once you have expanded the brackets you should think about how your terms relate to sin2x and cos2x 0
#4
(Original post by Muttley79)
Could you post your working so far?
Doesn't really matter. The equation I got to so far has been given up there ^
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#5
RDKGames help...?
Last edited by SeverusESnape; 1 year ago
0
1 year ago
#6
(Original post by SeverusESnape)
Could someone help with the following question?
Solve thefollowing in the interval -180° to 180°.
sinx ( cosx + cosecx ) = 2cos^2 x

You don't have to give the solutions but just simplify the equation for me. I got as far as cos^2 x + sinxcosx - sin^2 x. I just want to eliminate either cos or sin from the equation
Should have instead.

Now just apply the double angle formulae?
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#7
Yeah sorry that's what I got. But how do i proceed further? Which double angle formula?
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1 year ago
#8
(Original post by SeverusESnape)
Yeah sorry that's what I got. But how do i proceed further? Which double angle formula?
sin(2x) can be used on the middle term.

cos(2x) can be used on the two leftover terms.

Do you see it??
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#9
(Original post by RDKGames)
sin(2x) can be used on the middle term.

cos(2x) can be used on the two leftover terms.

Do you see it??
Yeah I totally do but I don't see how that would help me get my solutions for x..?
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1 year ago
#10
(Original post by SeverusESnape)
Yeah I totally do but I don't see how that would help me get my solutions for x..?
The point is that you use these to get an eqn in tan(2x)
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#11
(Original post by RDKGames)
The point is that you use these to get an eqn in tan(2x)
AHHH ok thanks a lot!!
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