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16 March 2017
Solution:
Cot2x-tan78=1/2(secxsec78)
simplifying everything into sine and Cosine.
Cos2x/sin2x-sin78/cos78=1/2(secx.1/cos78).
Crossing cos78 from right to left and sin2x from the left to the right
Then we have cos2xcos78-sin2xsin78=sin2x/2cosx.
The right hand can simplify to become cos(2x+78)=sin2x/2cosx
recall that sin2x=sin(x+x)=sinxcosx+cosxsinx=2sinxcosx...now applying it here now we have
cos(2x+78)=2sinxcosx/2cosx
cos(2x+78)=sinx
and sinx=cos(90-x)
cos(2x+78)=cos(90-x)
taking inverse of both sides by multiply it by cos inverse then we have
2x+78=90-x
3x=12
x=4.
I would prefer error correction in my solution,if you spotted any.
16 March 2017
And to add to the solution,following answers would also suit,
2x+78=270+x => x=192
2x+78 = 450-x => x=124
2x+78=810-x => x=244
16 March 2017
Answers are a x=4,12 and 64 degrees according to my solution method
10 April 2017
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