SPM Additional Mathematics 2019, Paper 2 (Question 10)


Question 10:
( a )(i) Prove tan A 2 = 1cosA sinA . ( ii )  Hence, without using calculator, find the value of tan15 o .       State your answer in the form p q  , where p and q are       constants. (b)( i ) Sketch the graph of y= 3 2 sinA for 0A2π. ( ii ) Hence, using the same axes, sketch a suitable straight          line to find the number of solutions for the equation         ( cot A 2 )( 1cosA )= A 2π  for 0A2π.        State the number solutions.

Solution:
(a)(i)
Right hand side, 1cosA sinA = 2 sin 2 A 2 2sin A 2 cos A 2              = sin A 2 cos A 2             =tan A 2             =( Left hand side )

(a)(ii)
tan( 30 2 )= 1cos 30 o sin 30 o tan 15 o = 1 3 2 1 2           = 2 3 2 1 2          =2 3

(b)(i)




(b)(ii)
( cot A 2 )( 1cosA )= A 2π 1 tan A 2 ( 1cosA )= A 2π ( sinA 1cosA )( 1cosA )= A 2π sinA= A 2π 3 2 sinA= A 2π ×( 3 2 ) y= 3A 4π


Number of solutions = 3

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