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cos q = 1/2 (a+1/a) then cos 3q in term of `a` is A) 1/4(a³+1/a³). B). 1/2(a³+1/a³). C) 4(a³+1/a³). D) none of these

cos q = 1/2 (a+1/a) then cos 3q in term of `a` is A) 1/4(a³+1/a³). B). 1/2(a³+1/a³). C) 4(a³+1/a³). D) none of these

Grade:12th pass

1 Answers

Saurabh Dubey
25 Points
4 years ago
Given: cosx =( 1/2)[a + (1/a )].........(1)so , [ a + ( 1/a) ] = 2cosx.........(2)from equation (1)cos³x = (1/2)³ [a +(1/a)]³cos³x = (1/8) [ a³ +(1/a³) + 3.a.(1/a){a+(1/a)]8cos³x = a³ +(1/a³) + 3[ a + (1/a) ]from equation (2) put the value of [ a+(1/a)]8cos³x = a³ + (1/a³) + 3× 2cosx 8cos³x - 6cosx = a³ +(1/a³).......(3)Divide by 2 both sides of equation (3)4cos³x - 3cosx = (1/2)[a³ +(1/a³)]now we know that cos3x = 4cos³x - 3 cosxcos 3x = (1/2) [ a³ + (1/a³)]so correct option is (B)

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