56{}^\circ +\cos 58{}^\circ -\cos 66{}^\circ \] \[=2{{\cos }^{2}}28{}^\circ +2\sin 62{}^\circ .\sin 4{}^\circ \] \[=2{{\cos }^{2}}28{}^\circ +2\cos 28{}^\circ .\sin 4{}^\circ \] \[=2\cos 28{}^\circ (\cos 28{}^\circ +\cos 86{}^\circ )\] \[=2\cos 28{}^\circ .2\cos 57{}^\circ \cos 29{}^\circ \] \[=4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ \]. Aliter: Apply the conditional identity \[\cos A+\cos B-\cos C=-1+4\cos \frac{A}{2}\cos \frac{B}{2}\sin \frac{C}{2}\]\[[\because \,56{}^\circ +58{}^\circ +66{}^\circ =180{}^\circ ]\] We get the VALUE of REQUIRED expression equal to\[4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ \].

"> 56{}^\circ +\cos 58{}^\circ -\cos 66{}^\circ \] \[=2{{\cos }^{2}}28{}^\circ +2\sin 62{}^\circ .\sin 4{}^\circ \] \[=2{{\cos }^{2}}28{}^\circ +2\cos 28{}^\circ .\sin 4{}^\circ \] \[=2\cos 28{}^\circ (\cos 28{}^\circ +\cos 86{}^\circ )\] \[=2\cos 28{}^\circ .2\cos 57{}^\circ \cos 29{}^\circ \] \[=4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ \]. Aliter: Apply the conditional identity \[\cos A+\cos B-\cos C=-1+4\cos \frac{A}{2}\cos \frac{B}{2}\sin \frac{C}{2}\]\[[\because \,56{}^\circ +58{}^\circ +66{}^\circ =180{}^\circ ]\] We get the VALUE of REQUIRED expression equal to\[4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ \].

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\[1+\cos \,{{56}^{o}}+\cos \,{{58}^{o}}-\cos {{66}^{o}}=\] [IIT 1964]

Mathematics Trigonometric Identities in Mathematics . 5 months ago

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\[1+\cos 56{}^\circ +\cos 58{}^\circ -\cos 66{}^\circ \] \[=2{{\cos }^{2}}28{}^\circ +2\sin 62{}^\circ .\sin 4{}^\circ \] \[=2{{\cos }^{2}}28{}^\circ +2\cos 28{}^\circ .\sin 4{}^\circ \] \[=2\cos 28{}^\circ (\cos 28{}^\circ +\cos 86{}^\circ )\] \[=2\cos 28{}^\circ .2\cos 57{}^\circ \cos 29{}^\circ \] \[=4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ \]. Aliter: Apply the conditional identity \[\cos A+\cos B-\cos C=-1+4\cos \frac{A}{2}\cos \frac{B}{2}\sin \frac{C}{2}\]\[[\because \,56{}^\circ +58{}^\circ +66{}^\circ =180{}^\circ ]\] We get the VALUE of REQUIRED expression equal to\[4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ \].

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Posted on 01 Aug 2024, this text provides information on Mathematics related to Trigonometric Identities in Mathematics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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