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Trigonometric Ratios of Multiples of an Angle

In Δ ABC, rig...

Question

In ΔABC, right angled at B. If, find the value of

(i) sin A cos C + cos A sin C

(ii) cos A cos C − sin A sin C

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Solution

If BC is k, then AB will be, where k is a positive integer.

In ΔABC,

AC² = AB² + BC²

=

= 3k² + k² = 4k²

∴ AC = 2k

(i) sin A cos C + cos A sin C

(ii) cos A cos C − sin A sin C

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