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CBSE Class 11-science Answered

If sin ^2A=x then express the values of sin A . sin 2A . sin 3A . sin 4A in terms of x.
Asked by tps.mjmdr | 16 Jun, 2018, 08:11: PM
answered-by-expert Expert Answer
sinA sin2A sin3A sin4A where sin2 A = x
using sin2A = 2sinAcosA, sin3A = 3sinA - 4sin3 A, sin4A = 2sin2Acos2A = 4 sinAcosA(1 - 2sin2 A)
sin A . sin 2A . sin 3A . sin 4A = sinA 2sinAcosA (3sinA - 4sin3 A) 4 sinAcosA(1 - 2sin2 A)
                                           = 8sin3A cos2A(3sinA - 4sin3 A)(1 - 2sin2 A)
                                           = 8sin3A (1 - sin2A)(3sinA - 4sin3 A)(1 - 2sin2 A)
                                           = 8sin4A(1 - sin2A)(3 - 4sin2 A)(1 - 2sin2 A)
                                           = 8x2 (1 - x)(3 - 4x)(1 - 2x)
Answered by Sneha shidid | 18 Jun, 2018, 12:55: PM
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