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SPM Additional Mathematics 2019, Paper 2 (Question 10)


Question 10:
(a)(i) Prove tanA2=1cosAsinA.(ii) Hence, without using calculator, find the value of tan15o.      State your answer in the form pq , where p and q are      constants.(b)(i) Sketch the graph of y=32sinA for 0A2π.(ii) Hence, using the same axes, sketch a suitable straight         line to find the number of solutions for the equation        (cotA2)(1cosA)=A2π for 0A2π.       State the number solutions.

Solution:
(a)(i)
Right hand side,1cosAsinA=2sin2A22sinA2cosA2             =sinA2cosA2            =tanA2            =(Left hand side)

(a)(ii)
tan(302)=1cos30osin30otan15o=13212          =23212         =23

(b)(i)




(b)(ii)
(cotA2)(1cosA)=A2π1tanA2(1cosA)=A2π(sinA1cosA)(1cosA)=A2πsinA=A2π32sinA=A2π×(32)y=3A4π


Number of solutions = 3

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