Prove that- 7 - 12-cos- 12-sin 5 - 12-sin- 12

105 #176;=7 #960;12, #160;15 #176;= #960;12, #160;75 #176;=5 #960;12, #160;15 #176;= #960;12 LHS = cos105o + cos15o nbsp; nbsp; nbs ...

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Relation between Trigonometric Ratios

Prove that: 7...

Question

Prove that: $\frac{7 π}{12} + \cos \frac{π}{12} = \sin \frac{5 π}{12} - \sin \frac{π}{12}$

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Solution

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\cos \frac{π}{12} - \sin \frac{π}{12}

\sin \frac{5 π}{18} - \cos \frac{4 π}{9} = \sqrt{3} \sin \frac{π}{9}

\cos \frac{π}{12} - \sin \frac{π}{12} = \frac{1}{\sqrt{2}}

X = sin (θ + \frac{7 π}{12}) + sin (θ - \frac{π}{12}) + sin (θ + \frac{3 π}{12}), Y = cos (θ + \frac{7 π}{12}) + cos (θ - \frac{π}{12}) + cos (θ + \frac{3 π}{12}),

\frac{X}{Y} - \frac{Y}{X} = 2 tan 2 θ .

(3 - \sqrt{5})

\frac{2 \sqrt{2}}{3}

(5 - \sqrt{3})

\frac{3 \sqrt{3}}{5}

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