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C4 problem Where am I going wrong?

This is a composite angle formula question, and I keep getting the answer wrong! Can anyone tell me what I'm doing wrong/how to fix it

sin(45-X) = CosX

Sin45CosX-Cos45SinX=CosX

Change into trig ratio

sqrt2/2CosX - sqrt2/2sinX=CosX

Divide through by Cosx

sqrt2/2 -sqrt2/2.tanX =1

sqrt2/2(1-tanx)=1

1-tanx = 2/sqrt2

tanx= 1-2/sqrt2

x=-22.5

but this is not the correct answer, the correct answer is supposed to be 157.5???

(edited 8 years ago)

Reply 1

PS4

Tanx = 1 - 2/sqrt2 (you rearranged it wrong :smile:

)

Reply 2

TeeEm

too slow ...
this by the way can be done very quickly without any compound angles or a calculator!

Reply 3

KateAteKarrots

Original post by PS4

Tanx = 1 - 2/sqrt2 (you rearranged it wrong :smile:

)

oh silly me, i corrected it! thanks!

however, that rearrangement gives me -22.5? which still isn't right!

Reply 4

KateAteKarrots

Original post by KateAteKarrots

oh silly me, i corrected it! thanks!

however, that rearrangement gives me -22.5? which still isn't right!

]

never mind, i understand what i did now! i need to use cast! thanks so much for help

Reply 5

atsruser

Original post by TeeEm

too slow ...
this by the way can be done very quickly without any compound angles or a calculator!

u=\frac{45}{2}-x

Reply 6

atsruser

Original post by KateAteKarrots

]

never mind, i understand what i did now! i need to use cast! thanks so much for help

Yes, use CAST. I guess you were given a range in which to find the solutions? If so, use CAST to guide you, or draw out the periodic graphs of the appropriate functions to make it clear where the solutions will lie.