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Question Number 86231 by liki last updated on 27/Mar/20

Commented by liki last updated on 27/Mar/20

$$..plzineedhelpqnno.5\left(a\right)\mathrm{\&}c$$

Answered by TANMAY PANACEA. last updated on 27/Mar/20

$$\frac{tan145-tan125}{1+tan145tan125}$$$$=tan(145-125)$$$$=tan20$$$$=cot70$$$$=\frac{1}{tan70}$$$$=\frac{1-{tan}^{2}35}{2tan35}$$$$=\frac{1-x^2}{2x}$$

Commented by liki last updated on 27/Mar/20

$$....Thankyousomuch$$

Answered by TANMAY PANACEA. last updated on 27/Mar/20

$$cosx+cosy=cosa$$$$sinx+siny=sina$$$$a=\frac{7\pi }{12}={105}^o$$$$from1)2cos\frac{x+y}{2}cos\frac{x-y}{2}=cosa$$$$from2)2sin\frac{x+y}{2}cos\frac{x-y}{2}=sina$$$$tan\left(\frac{x+y}{2}\right)=tana$$$$x+y=2a=\frac{7\pi }{6}={210}^o$$$$4{cos}^2\frac{x+y}{2}{cos}^2\frac{x-y}{2}+4{sin}^2\frac{x+y}{2}{cos}^2\frac{x-y}{2}=1$$$$4{cos}^2\frac{x-y}{2}({cos}^2\frac{x+y}{2}+{sin}^2\frac{x+y}{2})=1$$$$cos\frac{x-y}{2}=\pm \frac{1}{2}$$$$cos\left(\frac{x-y}{2}\right)=\frac{1}{2}=cos\frac{\pi }{3}$$$$x-y={120}^o$$$$x+y={210}^o$$$$2x={330}^{o}x={165}^o$$$$y={45}^o$$$$nowif$$$$cos\left(\frac{x-y}{2}\right)=\frac{-1}{2}=cos{120}^o$$$$x-y={240}^o\mathit{b}\mathit{u}\mathit{t}\mathit{l}\mathit{o}\mathit{o}\mathit{k}$$$$\mathit{x}+\mathit{y}={210}^{\mathit{o}}\mathit{b}\mathit{u}\mathit{t}\mathit{x}-\mathit{y}={240}^{\mathit{o}}$$$$\mathit{s}\mathit{o}\mathit{c}\mathit{o}\mathit{s}\left(\frac{\mathit{x}-\mathit{y}}{2}\right)\ne \frac{-1}{2}$$$$plscheck...$$$$$$

Commented by liki last updated on 27/Mar/20

$$...Beblessedsir,iunderstoodwell!$$

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