Solution : The formula of cos C + cos D is 2 cos(\(C + D\over 2\)) cos(\(C โ D\over 2\)). Example : Express cos \(4\theta\) + cos \(8\theta\) as a product. Solution : We have, cos \(4\theta\) + cos \(8\theta\) = 2 cos(\(8\theta + 4\theta\over 2\)) cos(\(8\theta โ 4\theta\over 2\)) = 2 cos \(6\theta\) cos โฆ
Solution : The formula of sin C โ sin D is 2 sin(\(C โ D\over 2\)) cos(\(C + D\over 2\)). Example : Express sin \(6\theta\) โ sin \(2\theta\) as a product. Solution : We have, sin \(6\theta\) โ sin \(2\theta\) = 2 sin(\(6\theta โ 2\theta\over 2\)) cos(\(6\theta + 2\theta\over 2\)) = 2 sin \(2\theta\) cos โฆ
Solution : The formula of sin C + sin D is 2 sin(\(C + D\over 2\)) cos(\(C โ D\over 2\)). Example : Express sin \(4\theta\) + sin \(2\theta\) as a product. Solution : We have, sin \(4\theta\) + sin \(2\theta\) = 2 sin(\(4\theta + 2\theta\over 2\)) cos(\(4\theta โ 2\theta\over 2\)) = 2 sin \(3\theta\) cos โฆ
Solution : The formula of 2 sin A sin B is cos (A โ B) โ cos (A + B). Example : Solve : 2 sin 75 sin 15. Solution : We have, 2 sin 75 sin 15 = cos (75 โ 15) โ cos (75 + 15) = cos 60 โ cos 90 = โฆ
Solution : The formula of 2 cos A cos B is cos (A + B) + cos (A โ B). Example : Solve : 2 cos 75 cos 15. Solution : We have, 2 cos 75 cos 15 = cos (75 + 15) + cos (75 โ 15) = cos 90 + cos 60 = โฆ
Solution : The formula of 2 cos A sin B is sin (A + B) โ sin (A โ B). Example : Solve : 2 cos 75 sin 15. Solution : We have, 2 cos 75 sin 15 = sin (75 + 15) โ sin (75 โ 15) = sin 90 โ sin 60 = โฆ
Solution : The formula of 2 sin A cos B is sin (A + B) + sin (A โ B). Example : Solve : 2 sin 75 cos 15. Solution : We have, 2 sin 75 cos 15 = sin (75 + 15) + sin (75 โ 15) = sin 90 + sin 60 = โฆ
Solution : The value of tan 75 degrees is \(\sqrt{3} + 1\over \sqrt{3} โ 1\). Proof :ย We write tan 75 as tan (45 + 30). Using the formula of tan (A + B), tan 75 = tan (45 + 30) = \(tan 45 + tan 30\over 1 โ tan 45 tan 30\) \(\implies\) tan โฆ
Solution : The value of tan 15 degrees is \(\sqrt{3} โ 1\over \sqrt{3} + 1\). Proof :ย We write tan 15 as tan (45 โ 30). Using the formula of tan (A โ B), tan 15 = tan (45 โ 30) = \(tan 45 โ tan 30\over 1 + tan 45 tan 30\) \(\implies\) tan โฆ
Solution : The formula of tan (A + B + C) is \(tan A + tan B + tan C โ tan A tan B tan C\over 1 โ tan A tan B โ tan B tan C โ tan C tan A\). Proof : We have, tan (A + B + C) = tan((A โฆ
