The value of sin 1-sin 3-sin 5-sin 7-cos 1-cos 2-sin 4- is

Sin1^∘+sin3^∘+sin5^∘+sin7^∘cos1^∘cos2^∘sin4^∘ =(sin1^∘+sin3^∘)+(sin5^∘+sin7^∘)cos1^∘cos2^∘sin4^∘ nbsp;= 2sin 2^∘cos 1^∘+2sin 6^∘cos 1^∘cos1^∘cos2^∘sin4^∘ ...

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Byju's Answer

Standard XII

Mathematics

Product of Trigonometric Ratios in Terms of Their Sum

The value of ...

Question

The value of $\frac{sin 1^{\circ} + sin 3^{\circ} + sin 5^{\circ} + sin 7^{\circ}}{cos 1^{\circ} cos 2^{\circ} sin 4^{\circ}}$ is

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Solution

$\frac{sin 1^{\circ} + sin 3^{\circ} + sin 5^{\circ} + sin 7^{\circ}}{cos 1^{\circ} cos 2^{\circ} sin 4^{\circ}} = \frac{(sin 1^{\circ} + sin 3^{\circ}) + (sin 5^{\circ} + sin 7^{\circ})}{cos 1^{\circ} cos 2^{\circ} sin 4^{\circ}} = \frac{2 sin 2^{\circ} cos 1^{\circ} + 2 sin 6^{\circ} cos 1^{\circ}}{cos 1^{\circ} cos 2^{\circ} sin 4^{\circ}} = \frac{2 (sin 2^{\circ} + sin 6^{\circ})}{cos 2^{\circ} sin 4^{\circ}} = \frac{4 sin 4^{\circ} cos 2^{\circ}}{cos 2^{\circ} sin 4^{\circ}} = 4$

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The value of sin1∘+sin3∘+sin5∘+sin7∘cos1∘cos2∘sin4∘ is

sin1∘+sin3∘+sin5∘+sin7∘cos1∘cos2∘sin4∘=(sin1∘+sin3∘)+(sin5∘+sin7∘)cos1∘cos2∘sin4∘=2sin2∘cos1∘+2sin6∘cos1∘cos1∘cos2∘sin4∘=2(sin2∘+sin6∘)cos2∘sin4∘=4sin4∘cos2∘cos2∘sin4∘=4

The value of $\frac{sin 1^{\circ} + sin 3^{\circ} + sin 5^{\circ} + sin 7^{\circ}}{cos 1^{\circ} cos 2^{\circ} sin 4^{\circ}}$ is